Butterflies, Pinwheels, and Wallpaper Unit Test Re …. 2. 3. Student: _ Date: _ Instructor:...

1.

2.

3.

Student: _____________________Date: _____________________

Instructor: Karen KaufmannCourse: Math 8 - Period 1

Assignment: Butterflies, Pinwheels, andWallpaper Unit Test Review

Which of these triangles are reflections of ?triangle ABC

Choose the correct answer below.

A. Triangle DEF, triangle GHJ, and triangle KMN are reflections of .triangle ABCB. of .Triangle GHJ is a reflection triangle ABCC. of .Triangle DEF and triangle GHJ are reflections triangle ABCD. of .Triangle DEF is a reflection triangle ABCE. Triangle KMN is a reflection of .triangle ABC

Which graph shows triangle ABC and its reflection across the y-axis, triangle A'B'C'?


A. B. C.

Describe in words how to map triangle ABC to its image triangle A'B'C'.

Which words below describe the mapping?

A. Triangle A'B'C' is the image of triangle ABC after a reflection across the y-axis.

B. Triangle A'B'C' is the image of triangle ABC translated 2 units horizontally.

C. Triangle A'B'C' is the image of triangle ABC after a reflection across the line x = − 2.

D. Triangle A'B'C' is the image of triangle ABC after a reflection across the x-axis.

-6 6

x

A

C

D

EF

G

J

K

N

-6

6y

B

H M

-6 6

x

A

C

A'

C'

-6

6y

B B'

-6 6

x

A

C

A'

C'

-6

6y

B

B'

-6 6

x

A

C

A'

B'C'

-6

6y

B

-6 6

x

A

C

A'

C'

0

6y

B B'

Butterflies, Pinwheels, and Wallpaper Unit Test Re-Karen Kau... https://xlitemprod.pearsoncmg.com/api/v1/print/math

1 of 61 2/26/16, 2:47 PM

4.

5.

Describe in words how to map triangle EFG to its image triangle E'F'G'. Use pencil and paper. Graph another reflection of triangle EFG.

Which words below describe the mapping?

A. Triangle E'F'G' is the image of triangle EFG after a reflection across the line y .= 2B. Triangle E'F'G' is the image of triangle EFG after a reflection across the y-axis.C. Triangle E'F'G' is the image of triangle EFG translated 2 units vertically. D. Triangle E'F'G' is the image of triangle EFG after a reflection across the x-axis.

Writing Which of the figures are reflections of the parallelogram ABCD? Use pencil and paper. Describe the reflections in words.

Which of the figures are reflections ABCD?

A. Parallelogram of parallelogram ABCD.

EFGH is a reflection

B. Parallelogram PQRS is a reflection of parallelogram ABCD.

C. Parallelogramof parallelogram ABCD.

s EFGH and JKLM arereflections

D. Parallelogram EFGH, JKLM, and PQRS are reflections of parallelogram ABCD.

E. Parallelogram of parallelogram ABCD.

JKLM is a reflection

-6 0

x

E

G

E'

G'

-6

6y

F

F'

-7 7

x

A

C

EF

G

J

L

PQ

R

DHM

S

-7

7y

B

K


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6. One image of triangle ABC is triangle A'B'C'. How do thex-coordinates of the vertices change? How do the y-coordinates of the vertices change? What type of reflection is the image triangleA'B'C'?

How do the x-coordinates of the vertices change?

A. The x-coordinates of the vertices are unchanged in the image.B. The x-coordinates of the vertices change differently depending on where they are on the figure.C. The x-coordinates of the vertices are the same distance away from the x-axis but in the opposite

direction.

D. The x-coordinates of the vertices are the same distance away from the y-axis but in the opposite direction.

How do the y-coordinates of the vertices change?

A. The y-coordinates of the vertices are unchanged in the image.B. The y-coordinates of the vertices change differently depending on where they are on the figure.C. The y-coordinates of the vertices are the same distance away from the x-axis but in the opposite

direction.

D. The y-coordinates of the vertices are the same distance away from the y-axis but in the opposite direction.

What type of reflection is the image triangle A'B'C'?

A. Triangle A'B'C' is the image of triangle ABC after a reflection across the line y .= − 2B. Triangle A'B'C' is the image of triangle ABC after a reflection across the x-axis.C. Triangle A'B'C' is the image of triangle ABC after a reflection across the line x .= − 2D. Triangle A'B'C' is the image of triangle ABC after a reflection across the y-axis.

-6 6

x

A

C

A'

C'

0

6y

B B'


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7.

8.

Your friend incorrectly says that the reflection of triangle EFG to its image triangle E'F'G' is a reflection across thex-axis. What is the correct reflection? What is your friend'smistake?

What is the correct description of the reflection?

A. Triangle E'F'G' is the image of triangle EFG after a reflection across the line y = − 5.

B. Triangle E'F'G' is the image of triangle EFG after a reflection across the line x = − 1.

C. Triangle E'F'G' is the image of triangle EFG after a reflection across the x-axis.

D. Triangle E'F'G' is the image of triangle EFG after a reflection across the line y = − 1.

What is your friend's mistake?

A. Your friend took the reflection across thex-axis instead of the y-axis.

B. Your friend took the reflection across thex-axis instead of the correct line of reflection.

C. Your friend took the reflection across they-axis instead of the x-axis.

(1) IIIIII

Which graph shows triangle ABC and its reflection across the x-axis, triangle A'B'C'? Use pencil and paper. Graph the reflection of triangle A'B'C' across the y-axis.

Graph I Graph II Graph III

Graph (1) shows triangle ABC and its reflection across the x-axis, triangle A'B'C'.

-8 -6 -4 -2 2

x

E

G

E'

G'

-10-8-6-4-2

2468

10y

F

F'

-6 6

x

-6

6y

A

BC

A'

B'C' -6 6

x

-6

6y

A

BC

A'

B'C'

-6 6

x

A'

C'

-6

6y

A

BC

B'


4 of 61 2/26/16, 2:47 PM

9.

10.

Think About the Process What is true about a figure and an image created by a reflection? One image of ABCD is A'B'C'D'. What type of reflection is the image A'B'C'D'?

What is true about a figure and an image created by a reflection? Select all that apply.

A. The figure and the image are the same size.B. For every reflection, each point on the image has the same x-coordinate as the corresponding

point in the figure.

C. The figure and the image are the same shape.D. For every reflection, each point on the image moves the same distance and direction from the

figure.

What type of reflection is the image A'B'C'D'?

A. A'B'C'D' is the image of ABCD after a reflection across the y-axis.B. A'B'C'D' is the image of ABCD after a reflection across the x-axis.C. A'B'C'D' is the image of ABCD after a reflection across the line x 1.= −D. A'B'C'D' is the image of ABCD after a reflection across the line y .= − 2

Your friend gives you the graph of ABCD and the image A'B'C'D'.What reflection produces the image A'B'C'D'? Use pencil and paper. Draw the image of ABCD using a reflection across a different line.

What reflection produces the image A'B'C'D'?

A. A'B'C'D' is the image of ABCD after a reflection across the line x .= 1B. A'B'C'D' is the image of ABCD after a reflection across the y-axis.C. A'B'C'D' is the image of ABCD after a reflection across the line y .= − 3D. A'B'C'D' is the image of ABCD after a reflection across the x-axis.

-7 7

x

A B

C

A'B'

C'D D'

0

6y

-10 10

x

A B

C

A'B'

C'D D'

0

6y


5 of 61 2/26/16, 2:47 PM

11.

12.

(1)

Challenge What reflection of the parallelogram ABCD results in the image A'B'C'D'? Use pencil and paper. Is the image unique using only one reflection? Is the image unique using one reflection and one translation?

Reflect ABCD across the line (1) =

yx

(1) ACB

Which of these graphs shows a transformation that is a rotation?

A B C

Graph (1) shows a transformation that is a rotation.

-8 -6 -4 -2 2 4 6 8

xDD'

-10-8-6-4-2

2468

10y

A

B'A'

C

B

C'

-10 -5 5 10

x

-10

-5

5

10y

-10 -5 5 10

x

-10

-5

5

10y

-10 -5 5 10

x

-10

-5

5

10y


6 of 61 2/26/16, 2:47 PM

13.

14.

(1) BAC

Which of these graphs shows a rotation of triangle PQR about the origin, (0,0)?

A B C

Graph (1) shows a rotation of triangle PQR about the origin, (0,0).

What is the angle of rotation about the origin, (0,0), that maps to ?triangle PQR triangle P Q R


A. 270°B. 180°C. 90°D. 360°

-10 -5 5 10

x

Q

R

-10

-5

5

10y

P

P

Q

R -10 -5 5 10

x

Q

R

Q

-10

-5

5

10y

PPR

-10 -5 5 10

x

Q

R

-10

-5

5

10y

P

P

Q

R

-8 -6 -4 -2 2 4 6 8

xP Q

R

R

-8

-6

-4

-2

2

4

6

8y

P

Q

O


7 of 61 2/26/16, 2:47 PM

15.

16.

Rotate triangle XYZ about the origin, (0,0).90°


A. B. C.

(1) ABC

Which of these graphs shows a rotation of triangle PQR about the origin, (0,0)? Use pencil and paper. How aretranslations, reflections, and rotations similar? How are they different? Include examples in your answer.

A B C


-8 -4 4 8

xY

-8

-4

4

8y

X

Z

-8 -4 4 8

xY

Y

Z

-8

-4

4

8y

X

Z

X

-8 -4 4 8

xY

XY

Z-8

-4

4

8y

X

Z

-8 -4 4 8

xY

-8

-4

4

8y

X

Z

X

Y

Z

-10 10

x

Q

R

Q

R

-10

10y

P

P-10 10

x

Q

R

-10

10y

PP

Q

R

-10 10

x

Q

R

-10

10y

P

P

Q

R


8 of 61 2/26/16, 2:47 PM

17.

18.

What is the angle of rotation about the origin, (0,0), that maps to ? Use pencil and paper. Explain why any rotation can be described by an angle between 0 and 360 .

triangle TRI triangle T R I

° °


A. 180°B. 270°C. 360°D. 90°

(1) II.III.IV.I.

Suppose triangle TRI is rotated about the origin, (0,0). In which quadrant is located? Make a graph showing triangle TRI and .

180° triangle T R Itriangle T R I

Given is located in quadrant (1) triangle T R I

Make a graph showing triangle TRI and . Choose the correct answer below.triangle T R I

A. B. C.

-8 -6 -4 -2 2 4 6 8

xR

I

R

I-8

-6

-4

-2

2

4

6

8y

T

T

O

-8 -4 4 8

x

-8

-4

4

8y

T

R

I

-8 -4 4 8

x

-8

-4

4

8y

T

R

I

T

R

I -8 -4 4 8

x

R

I

-8

-4

4

8y

T

R

I

T

-8 -4 4 8

x

-8

-4

4

8y

T

R

I

T

R

I


9 of 61 2/26/16, 2:47 PM

19.

20.

(1) ACB

Which of these graphs shows a rotation of triangle PQR about the origin, (0,0)? Use pencil and paper. For each graph that does not show a rotation of triangle PQR about the origin, (0,0), describe what transformation the graph does show.

A B C


Rotate rectangle KLMN about the origin, (0,0).270°


A. B. C.

-10 10

x

Q

R

Q

-10

10y

PPR

-10 10

x

Q

R

-10

10y

P

P

Q

R

-10 10

x

Q

R

Q

-10

10y

PP

R

-8 -4 4 8

xL

M

-8

-4

4

8y

K

N

-8 -4 4 8

xL

M N

M

-8

-4

4

8y

K

N

L

K

-8 -4 4 8

xL

M L

K

-8

-4

4

8y

K

N

N

M

-8 -4 4 8

xL

M M

N

-8

-4

4

8y

K

N

K

L


10 of 61 2/26/16, 2:47 PM

21.

22.

You want to find the angle of rotation about the origin, (0,0), that maps to . Draw an angle you could measure to do this. Find the angle of rotation.

triangle TRI triangle T R IWhich of these shows an angle you could measure to find the angle of rotation about the origin, (0,0)?

A. B.

C. D.

What is the angle of rotation about the origin, (0,0)?

A. 90°B. 180°C. 360°D. 270°

Rotate rectangle PQRS about the origin, (0,0). Use pencil and paper. Describe a different rotation for which the image of PQRS is the same as the image of PQRS after a rotation of about the origin.

90°

90°


A. B. C.

-8 -6 -4 -2 2 4 6 8

xR

I

I

-8

-6

-4

-2

2

4

6

8y

T

T

R

O

-8 8

x

I

-8

8y

TR

I

T

R

O

-8 8

x

I

-8

8y

TR

I

T

R

O

-8 8

x

I

-8

8y

TR

I

T

R

O

-8 8

x

I

-8

8y

TR

I

T

R

O

-8 -4 4 8

xP Q

RS

-8

-4

4

8y

-8 -4 4 8

xQ

RR

-8

-4

4

8y

P

S

P

Q

S

-8 -4 4 8

xQ

R

-8

-4

4

8y

P

S

S

RQ

P

-8 -4 4 8

xQ

R

-8

-4

4

8y

P

S

P Q

RS


11 of 61 2/26/16, 2:47 PM

23.

24.

Challenge Find three angles of rotation about the origin,(0,0), that map WXYZ to . Use pencil and paper. Does a negative angle of rotation make sense? If so, find three negative angles of rotation about the origin, (0,0), that map WXYZ to . If not, explain why not.

W X Y Z

W X Y Z

Select each angle of rotation about the origin, (0,0), that maps WXYZ to .W X Y Z

A. 90° B. 450°C. 900° D. 810°E. 360° F. 990°G. 270° H. 180°I. 1,080° J. 630°K. 720° L. 540°

Which graph could be a translation of triangle DEF?

Choose the correct graph below.

A. B. C.

-8 -6 -4 -2 2 4 6 8

x

W X

YZ

W

XY

Z

-8

-6

-4

-2

2

4

6

8y

O

0 2 4 6 8 10

xD

E

F

02

46

810

y

0 2 4 6 8 10

xD'

E'

F'

02

46

810

y

0 2 4 6 8 10

x

D'

E'

F'

02

46

810

y

0 2 4 6 8 10

xD'

E'

F'

02

46

810

y


12 of 61 2/26/16, 2:47 PM

25.

26.

27.

Triangle JKL has vertices J( , ), K( , ), and L( , ). Which graph shows triangle JKL and triangle J'K'L', its image after atranslation?

4 3 4 7 8 3


A. B.

C. D.

The coordinates of are , , and . If you translate units and units , what are the coordinates of '?

triangle DEF D(2,3) E(6,3) F(5,7) triangle DEF 3 left 4up D

The coordinates of ' are . (Type an ordered pair.)D

The vertices of parallelogram GRAM are and Graph GRAM and G'R'A'M', its image after a translation units right and up.

G( − 8,2), R( − 7,6), A( − 4,6), M( − 5,2).10 2 units


A. B.

C. D.

-10 0 10

xJ

K

LK'

L'

10y

J'

-10 0 10

xJ

K

L

10y

J'

K'

L'

-10 0 10

xJ

K

LJ'

K'

L'

10y

-10 0 10

xJ

K

L

10y

J'

K'

L'

-10 0 10

xG

R

10y

A

MG'

R' A'

M'

-10 0 10

xG

R

10y

A

MG'

R' A'

M'

-10 0 10

xG

R

M

10y

A

G'

R' A'

M'-10 0 10

xG

R

10y

A

M G'

R' A'

M'


13 of 61 2/26/16, 2:47 PM

28.

29.

Which graph could be a translation of triangle DEF? Use pencil and paper. Describe the translation in words.


A. B. C.

Triangle QRS is translated units and units . How do the x-coordinates of the vertices change? Explain. What are the coordinates of '?

4 left 3 upS

How do the x-coordinates of the vertices change?

A. The x-coordinates by because " " indicates a change.increase 4 left positiveB. The x-coordinates decrease by because is a positive number.4 4C. The x-coordinates by because " " indicates a change.decrease 4 left negativeD. The x-coordinates increase by because is a positive number.4 4

The coordinates of ' are . (Type an ordered pair.)S

D

E

-5-10

x

5

10y

F

-5-10

x

5

10y

D'

E'

F'

-5-10

x

5

10y

D'

E'

F' F'

-5-10

x

5

10y

D'

E'

0 5 10

xQ R

S

0

5

10y


14 of 61 2/26/16, 2:47 PM

30.

31.

(1) (2) (3)

Estimate the vertices of . If you translate units and units , what are the approximate coordinates of '?

triangle TUV triangle TUV 3 left 2up U

The coordinates of point T are about (1)

The coordinates of point U are about (2)

The coordinates of point V are about (3)

The approximate coordinates of ' are .U

( − 4, − 4).( − 6, − 6).( − 3, − 6).

( − 6, − 7).( − 5, − 3).( − 4, − 7).

( − 4, − 7).( − 5, − 3).( − 6, − 7).

(1) IIIIII

Which figure is the image of after atranslation? Use pencil and paper. Use arrow notation to show how each vertex of maps to its image after the translation.

triangle DEF

triangle DEFFigure (1) is the image of

after a translation.triangle DEF

T U

-10 -5V

x

-10

-5

y

-10 -8 -6 -4 -2 2 4 6 8 10

x

D

E

F

I II

III

-10

-8

-6

-4

-2

2

4

6

8

10y


15 of 61 2/26/16, 2:47 PM

32.

33.

Think About the Process What is true about a figure and an image created by a translation? The vertices of parallelogram GRAM are and Graph GRAM and G'R'A'M', its image after a translation units right and up.

G( − 10, − 8), R( − 9, − 5), A( − 5, − 5), M( − 6, − 8).13 1 unit

What is true about a figure and an image created by a translation? Select all that apply.

A. The figure and the image are the same size.B. The figure and the image are the same shape.C. Each point in the image moves the same distance and direction from the figure.D. Each point in the image has the same x-coordinate as the corresponding point in the figure.

Graph GRAM and G'R'A'M'. Choose the correct graph below.

A. B.

C. D.

Multiple Representations The vertices of parallelogram QUAD are and Graph QUAD and Q'U'A'D', its image after a translation units right and units up. Use pencil and graph

paper. Draw parallelogram QUAD and its image. Use arrows to show how each vertex is mapped to its image.

Q( − 8, − 8), U( − 7, − 4), A( − 4, − 4),D( − 5, − 8). 13 12


A. B. C.

-10 10

x

G

R A

M

R' A'

M'-10

y

G'

-10 10

x

G

R A

MG'

R' A'

M'-10

y

-10 10

x

G

R A R' A'

M'-10

y

M G'

-10 10

x

G

R A

M

R' A'

M'-10

y

G'

-10 10

xQ'

U' A'

D'

-10

10y

Q

U A

D

-10 10

xQ'

U' A'

D'

-10

10y

Q

U A

D

-10 10

x

Q

U A

D-10

10y

Q'

U' A'

D'


16 of 61 2/26/16, 2:47 PM

34.

35.

Challenge The vertices of pentagon VWXYZ are and Graph VWXYZ andV'W'X'Y'Z', its image after a translation units left and units up. Use pencil and graph paper. Sketch the figure and itsimage, then use the grid lines to estimate the distance between V and V'.

V(4, − 8), W(6, − 8), X(6, − 6), Y(5, − 5), Z(4, − 6).10 11

Graph VWXYZ and V'W'X'Y'Z'. Choose the correct graph below.

A. B. C.

Find the image of the letter for a reflection first across line L and then across line M. Is the resulting transformation a translation or a rotation? For a translation, describe the direction and distance. For a rotation, tell the center of rotation and the angle of rotation.

Which of the following shows the image in blue?

A. B. C.

Which of the following describes the resulting transformation?

A. It is a translation . The distance of the translation is the distance between L and M.to the leftB. It is a translation . The distance of the translation is twice the distance between L and

M.to the left

C. It is a rotation about a point halfway between L and M. The angle of rotation is counterclockwise.

180°

D. It is a rotation about a point halfway between L and M. The angle of rotation is clockwise.180°

M L

M L

-10 -5 5 10

xV W

XYZ

-10

-5

5

10y

V' W'

X'Y'Z'

-10 -5 5 10

x

V W

XYZ

-10

-5

5

10y

V' W'

X'Y'Z'

-10 -5 5 10

x

V' W'

X'Y'Z'

-10

-5

5

10y

V W

XYZ

Q


17 of 61 2/26/16, 2:47 PM

36.

37.


Which of the following shows the image in blue?

A. B. C.


A.

B. It is a translation . The distance of the translation is the distance between the letter and M.

down and to the right

C. It is a rotation about the point C. The angle of rotation is clockwise.78°D. It is a rotation about the point C. The angle of rotation is clockwise.156°

Identify the mapping as a translation, reflection, rotation, or glide reflection. Find the translation rule, reflection line, center of rotation and angle ofrotation, or glide translation rule and reflection line.

triangle triangle PQM→ KJN


A. The mapping is a glide reflection. The glide translation rule is (x,y) ( , ) and the reflection line is .

→ x y − 4x = 4

B. The mapping is a translation. The translation rule is (x,y) ( , ).→ x y − 4

C. The mapping is a reflection. The reflection line is .x = 4D. The mapping is a glide reflection. The glide translation rule is (x,y) ( , ) and the reflection

line is .→ x y + 4

x = 4

E. The mapping is a translation. The translation rule is (x,y) ( , ).→ x y + 4

F. The mapping is a rotation of 180 about the origin.°

It is a translation . The distance of the translation is twice the distance between the letter and M.

down and to the right

78°

78° 78° 78°

1 7

xA

B

C

D

EF M

N

P

Q-4

-2

2

4

yG

H

I

OJ

K

L


18 of 61 2/26/16, 2:47 PM

38.

39.

Identify the mapping as a translation, reflection, rotation, or glide reflection. Find the translation rule, reflection line, center of rotation and angle ofrotation, or glide translation rule and reflection line.

triangle triangle ABC→ HIF


A. The mapping is a glide reflection. The glide translation rule is (x,y) ( , ) and the reflection

line is .

→ x + 5 y

x = − 512

B. The mapping is a translation. The translation rule is (x,y) ( , ).→ x + 5 y

C. The mapping is a translation. The translation rule is (x,y) ( , ).→ x − 5 y

D.The mapping is a reflection. The reflection line is .x = − 5

12

E. The mapping is a rotation of 180 about the origin.°


Choose the correct image after the two transformations.

A. B. C.


A. It is a rotation about a point halfway between L and M. The angle of rotation is counterclockwise.

90°

B. It is a translation . The distance of the translation is twice the distance between L and M.

up and to the left

C. It is a translation . The distance of the translation is the distance between L and M.

up and to the left

D. It is a rotation about a point halfway between L and M. The angle of rotation is clockwise.90°

L

ML

M

L

M

1 7

xA

B

C

D

EF M

N

P

Q-4

-2

2

4

yG

H

I

OJ

K

L

T


19 of 61 2/26/16, 2:47 PM

40.

41.


Choose the correct image after the two transformations.

A. B. C.


A. It is a translation . The distance of the translation is the distance between the letter and M.

up and to the right

B. It is a rotation about the point C. The angle of rotation is clockwise.62°C. It is a rotation about the point C. The angle of rotation is clockwise.124°D. It is a translation . The distance of the translation is twice the distance

between the letter and M.up and to the right

Use the given points and lines to graph and its image after a reflection first across and then across . Is the resulting transformation a translation or a rotation? For a translation, describe the direction and distance. For a rotation,tell the center of rotation and the angle of rotation.

AB A B L1 L2

A( , ) and B( , ); : -axis; : -axis2 5 4 1 L1 y L2 x

Which of the following shows the image?

A. B. C. D.


A. It is a translation down and to the left. The distance of the translation is .1 unitB. It is a rotation about the origin. The angle of rotation is 180 .°C. It is a translation up and to the right. The distance of the translation is .1 unitD. It is a rotation about the midpoint of . The angle of rotation is 180 .AB °

62°C 62°C 62°C

VL

M62°

C

V

-6 6

xB

-6

6yA

A

B-6 6

xB

-6

6yA

B

A

-6 6

xB

-6

6yA

A

B

-6 6

xB

-6

6yA

B

A


20 of 61 2/26/16, 2:47 PM

42.

43.

Use the given points and lines to graph and its image after a reflection first across and then across . Is the resulting transformation a translation or a rotation? For a translation, describe the direction and distance. For a rotation,tell the center of rotation and the angle of rotation.

AB A B L1 L2

A( , ) and B( , ); : y ; : y3 − 5 − 4 − 3 L1 = 0 L2 = 1

Which of the following shows the image?

A. B. C. D.


A. It is a rotation about the midpoint of . The angle of rotation is 180 .AB °B. It is a translation up units.twoC. It is a rotation about the origin. The angle of rotation is 180 .°D. It is a translation up .one unit

For the coordinate grid to the right, identify a pair of congruent figures and write a congruence statement.

Which two triangles are congruent?

A. triangle trianglePCY ≅ XBN

B. triangle triangle HQT ≅ XNB

C. triangle triangle PCY ≅ NXB

D. triangle triangle HQT ≅ CYP

-6 6

x

-6

6y

AB A

B -6 6

x

-6

6y

AB

AB

-6 6

x

-6

6y

AB

BA

-6 6

x

-6

6y

AB B

A

-10 -8 -6 -4 -2 2 4 6 8 10

x

-10

-8

-6

-4

-2

2

4

6

8

10y

P

CY

X

BN

H

Q

T


21 of 61 2/26/16, 2:47 PM

44.

45.

For the coordinate grid to the right, identify a pair of congruent figures. Then determine a congruence transformation that maps the preimage to the congruent image.

Which two triangles are congruent?

A. triangle triangle HDM ≅ CAF

B. triangle triangle WQZ ≅ CFA

C. triangle triangle HDM ≅ QZW

D. triangle triangle WQZ ≅ ACF

Which congruence transformation maps the preimage to the congruent image? Select the correct choice below and fill in the answer boxes to complete your choice.

A. T ◦ r( )270°,O

B. T ◦ r( )180°,O

C. T (triangle H

D. T ◦ Rx = 2(tr

For the coordinate grid to the right, identify a pair of congruent figures. Then determine a congruence transformation that maps the preimage to the congruent image.

Which two figures are congruent?

A. ≅GC POB. ≅PO FDC. ≅GC FD

Which congruence transformation maps the preimage to the congruent image? Select the correct choice below and fill in the answer boxes to complete your choice.

A. T ◦ Ry-ax

B. T CG

C. Ry-axis ◦ T

,

,

,

,

-10 -8 -6 -4 -2 2 4 6 8 10

x

-10

-8

-6

-4

-2

2

4

6

8

10y

W

Q

Z

C

F

A

HD

M

,

,

,

-10 -8 -6 -4 -2 2 4 6 8 10

x

-10

-8

-6

-4

-2

2

4

6

8

10y

D

F

C

G

O

P


22 of 61 2/26/16, 2:47 PM

46.

47.

48.

49.

Determine whether the figures on the right are congruent. If so, describe a congruence transformation that maps one to the other. If not, explain.

If the figures are congruent, describe a congruence transformation that maps one to the other. Otherwise, explain why they are not congruent.

A. Yes. The congruence transformation is a reflection.B. Yes. The congruence transformation is a rotation.C. Yes. The congruence transformation is a translation.D. No. There is no congruence transformation that maps the figure on the left to the figure on the

right.

. Complete the congruence statement.ΔJKL ≅ ΔSTU

? ΔUTS ≅

ΔUTS ≅ ΔJ

K

L S

T

U

Name the corresponding parts of the congruent triangles.

∠A ≅ ∠∠B ≅ ∠

∠C ≅ ∠

side side AB ≅side side AC ≅side side BC ≅

A

B

C S

T

U

. Find the measure of the given angles.ΔABC ≅ ΔDEF

m∠A = x + 17m∠D = 2x

m∠A = °(Do not include the degree symbol in your answer.)

m∠D = °(Do not include the degree symbol in your answer.)


23 of 61 2/26/16, 2:47 PM

50.

51.

52.

53.

For the following parallelogram, the measure of C is . Find the measure of D, A, and B. Find the

length of and .

∠74° ∠ ∠ ∠

BC AB

The measure of D is .∠ °

The measure of A is .∠ °

The measure of B is .∠ °

The length of is .BC

The length of is .AB

The length of is and the length of is .AD 17 DC 6

A B

CD

The perimeter of the parallelogram to the right is . The length of side is . Find the lengths of , , and .

65.8JM 5.7 KL JK ML

The length of is .KL

The length of is .JK

The length of is .ML

J

K

L

M

For the parallelogram, AB and Find the lengths of and .

= 11 BD = 14.AC ED

The length of the diagonal is .AC

The length of the diagonal is .ED

The pair of triangles is congruent. List the corresponding angles and the corresponding sides.

List the corresponding angles.

∠3 and ∠ ∠1 and ∠ ∠2 and ∠List the corresponding sides.

andCA andAB andBC

AD

B

EC

C

A

B D

E

F3

1

2 4

5

6


24 of 61 2/26/16, 2:47 PM

54.

55.

56.


T

Y W

25

6 4



andTU andUS andST


M

N

L S

T

R2

3

1 5

6

4



andMN andNL andLM

Use the translation to graph the image of (x,y)→(x + 3,y − 1) ΔD'E'F'.

Graph and Choose the correct graph below.ΔDEF ΔD'E'F'.

A. B. C.

U

S X

3

1

-5 5

x

-5

5y

D

E

F

-5 5

x

-5

5y

-5 5

x

-5

5y

-5 5

x

-5

5y


25 of 61 2/26/16, 2:47 PM

57.

58.

Farmland A farmer has a rectangular plot of land shaped like the figure in the graph. There is another identical plot of land yards east and yards north of the original plot. Graph both plots of land. Then find the combined area of the two plots of land.

120 100

Graph both plots of land. Choose the correct graph below.

A. B. C.

The combined area of the plots is square yards.

Describe the location of the image of the figure under the given translation relative to the original figure. Then graph the image.

(x,y) (x ,y )→ + 5 + 3

Describe the location of the image compared to the original figure.

A. The image is down and to the left.B. The image is up and to the left.C. The image is down and to the right.D. The image is up and to the right.

Graph the figure and the image under the given translation. Choose the correct graph below.

A. B. C.

0 120 240

x0

120

240y

0 120 240

x0

120

240y

0 120 240

x0

120

240y

0 120 240

x0

120

240y

-10 -8 -6 -4 -2 2

x

-3

3

6y

-10 -5 5

x

-8

-4

4

8y

-10 -5 5

x

-2

5

10y

2-16 -12 -8 -4

x

-8

-4

4

8y


26 of 61 2/26/16, 2:47 PM

59.

60.

The image of a parallelogram is given. Use the translation to find the coordinates of . Then graph the original parallelogram and the image.

(x,y)→(x + 3,y − 2)Q

The coordinates of are . (Type an ordered pair.)Q

Graph QRST and Q'R'S'T'. Choose the correct graph below.

A. B. C.

Figure II is a translation image of Figure I. Write a rule to describe the translation.

The translation rule is (x,y) (x ,y ).→ + ( ) + ( )

-5 5

x

-5

5y

T' S'

R'Q'

-5 5

x

-5

5y

-5 5

x

-5

5y

-5 5

x

-5

5y

-6 -3 3 6

x

-6

-3

3

6y

II

I


27 of 61 2/26/16, 2:47 PM

61.

62.

Error Analysis The blue figure is the image of the black figure after a translation. Your friend says that a rule that describes the translation is (x,y) (x ,y ). What is the correct rule? What mistake did your friend likely make?

→ + 1 − 2

Which is the correct rule for the translation?

A. (x,y) (x ,y)→ − 1

B. (x,y) (x ,y )→ + 2 − 1

C. (x,y) (x ,y )→ − 1 + 2

D. (x,y) (x,y )→ + 2

What mistake did your friend likely make?

A. Your friend wrote a rule that describes the horizontal change but not the vertical change.B. Your friend wrote a rule that describes the vertical change but not the horizontal change.C. Your friend wrote a rule that describes the translation from the blue figure to the black figure.D. Your friend reversed the horizontal and vertical changes.

Think About the Process Why should you choose W andW' to help you write a rule that describes the translation from WXYZ to W'X'Y'Z'? Write a rule that describes the translation.

Which of these rules describes the translation?

A. (x,y) (x ,y )→ + 9 − 10

B. (x,y) (x ,y )→ − 9 + 10

C. (x,y) (x ,y )→ − 10 + 9

D. (x,y) (x ,y )→ + 10 − 9

-6 -3 3 6

x

-6

-3

3

6y

-10 -8 -6 -4 -2 2 4 6 8 10

x

W X

YZ

-10

-8

-6

-4

-2

2

4

6

8

10y

W' X'

Y'Z'


28 of 61 2/26/16, 2:47 PM

63.

64.

65.

Challenge Write a rule describing the translation from to . Then write a rule describing the

translation from to . Use pencil and paper. Write a rule describing the translation from to

VWXY V'W'X'Y'V'W'X'Y' V''W''X''Y''

VWXY V''

Which rule describes the translation from to ?VWXY V'W'X'Y'

A. (x,y) (x ,y )→ + 1 − 12

B. (x,y) (x ,y )→ + 12 + 1

C. (x,y) (x ,y )→ − 1 + 12

D. (x,y) (x ,y )→ + 1 + 12

Which rule describes the translation from to V'W'X'Y' V''W''X''Y

A. (x,y) (x ,y )→ − 10 + 1

B. (x,y) (x ,y )→ + 1 + 10

C. (x,y) (x ,y )→ + 10 + 1

D. (x,y) (x ,y )→ + 1 − 10

The vertices of ABC are , , and . If ABC is reflected across the y-axis to produce the image A'B'C', find the coordinate of the vertex '.

Δ A( − 4,4) B( − 2,4) C( − 3,2) ΔΔ A

The coordinates of ' are . A(Type an ordered pair.)

The vertices of trapezoid ABCD are , , , and . Graph ABCD and A'B'C'D', its image after a reflection across the -axis.

A(2, − 3) B(5, − 3) C(6, − 7) D(1, − 7)y

Which graph shows ABCD and A'B'C'D'?

A. C.

-10 -8 -6 -4 -2 2 4 6 8 10

x

V

W X

Y

V'

W' X'

Y'V''

W'' X''

Y''

-10

-8

-6

-4

-2

2

4

6

8

10y

B.

-10 10

x

-9

9y

A B

CD

A'B'

C' D'

-10 10

x

-9

9y

A B

CD

A' B'

C'D'

-10 10

x

-9

9y

A B

CD

A'B'

C' D'


29 of 61 2/26/16, 2:47 PM

66.

67.

68.

Kite Making You fold a large piece of cardboard in half to make a kite. The vertices of are , , and . Graph ABC and A'B'C', its image after a reflection across the -axis.

ΔABC A(0,5) B(4,0)C(0, − 6) Δ Δ y

Which graph shows ABC and A'B'C'?Δ Δ

A. B. C.

Mental Math The rectangle ABCD is reflected across the -axis. What are the coordinates of the vertex '?

xC

The coordinates of ' are . C(Type an ordered pair.)

Think About the Process Given points J( , ), A( , ), and R( , ), graph and its image after a reflection across the line x . What effect does a reflection have on a figure?

4 4 7 5 5 2 ΔJAR= − 1


A. B. C. D.


A. A reflection changes only a figure's shape, not its position or size. B. A reflection changes a figure's position, size, and shape. The image of the figure faces the

opposite direction as the figure.

C. A reflection changes only a figure's position, not its size or shape. The image of the figure faces the same direction as the figure.

D. A reflection changes only a figure's position, not its size or shape. The image of the figure faces the opposite direction as the figure.

-7 7

xBB'

-7

7y

A

C

A'

C'

-7 7

x

-7

7y

A

B

C

A'

B'

C'

-7 7

xBB'

-7

7y

A

CA'

C'

-2 2 4 6

x

A B

CD

-2

2

4

6y

-10 10

x

JA

R

J'R'

A'-1

9y

-10 10

x

JA

R

J'A'

R'-1

9y

-10 10

x

JA

R

J'A'

R'

-1

8y

-10 10

x

JA

R

J'A'

R'-1

9y


30 of 61 2/26/16, 2:47 PM

69.

70.

71.

The vertices of ABC are , , and . If ABC is reflected across the line y to produce the image A'B'C', find the coordinates of the vertex '. Use pencil and paper. Find the coordinates of the vertex ' if

ABC is reflected across the line x .

Δ A( − 4,5) B( − 2,3) C( − 5,3) Δ = − 2Δ A A

Δ = − 2

The coordinates of ' after a reflection across the line y are . A = − 2(Type an ordered pair.)

Challenge The vertices of ABC are , , and . ABC is reflected across the y-axis and then reflected across the x-axis to produce the image A''B''C''. Graph and .

Δ A( − 5,5) B( − 2,3) C( − 4,3) ΔΔ ΔABC ΔA''B''C''

Which graph shows and ?ΔABC ΔA''B''C''

A. B. C.

Point has coordinates . If you rotate about theorigin, (0,0), what are the coordinates of ?

S (2,3) S 270°S

The coordinates of are .S(Type an ordered pair.)

-6 6

x

-6

6y

A

BC

A''

B''C''

-6 6

x

A''

C''

-6

6y

A

BC

B''-6 6

x

-6

6y

A

BC

A''

B''C''

-8 -6 -4 -2 2 4 6 8

x

S

-8

-6

-4

-2

2

4

6

8y


31 of 61 2/26/16, 2:47 PM

72.

73.

74.

Rotate triangle PQR about the origin, (0,0).90°


A. B. C.

Error Analysis Point has coordinates . On a quizyesterday, incorrectly claimed that if you rotate

about the origin, (0,0), the coordinates of are . Find the correct coordinates of . What was

's likely error?

N (5,2)Ari

N 90° N(2, − 5) NAri

The coordinates of are .N(Type an ordered pair.)

What was 's likely error?Ari

A. translated units left.He N 5B. rotated about the origin, (0,0).He N 270°C. reflected across the x-axis.He ND. translated units down.He N 2E. rotated about the origin, (0,0).He N 180°F. reflected across the y-axis.He N

Windmill An architect is designing a new windmill with four sails. In h sketch, the sails' center of rotation is the origin,(0,0), and the tip of one of the sails, point , has coordinates . wants to make another sketch that shows the windmill after the sails have rotated about their center of rotation. What would be the coordinates of ?

erQ (4,2) She

180° Q

The coordinates of would be .Q(Type an ordered pair.)

-8 -4 4 8

xPQ

R

-8

-4

4

8y

-8 -4 4 8

x

Q

R

-8

-4

4

8y

P -8 -4 4 8

x

-8

-4

4

8y

P

Q

R-8 -4 4 8

x

Q

-8

-4

4

8y

P

R

-8 -6 -4 -2 2 4 6 8

x

N

-8

-6

-4

-2

2

4

6

8y


32 of 61 2/26/16, 2:47 PM

75.

76.

Suppose triangle PQR is rotated about the origin, (0,0). Find the coordinates of , , and . Then sketch .

180°P Q R triangle P Q R

The coordinates of are . (Type an ordered pair.)P

The coordinates of are . (Type an ordered pair.)Q

The coordinates of are . (Type an ordered pair.)R

Which of these graphs shows ?triangle P Q R

A. B. C.

(1)

Point has coordinates . If you rotate about the origin, (0,0), what are the coordinates of ? How could you rotate to get back to ? Use pencil and paper. Give two other ways to rotate to get to .

T (4,5) T 90° TT T T T

The coordinates of are .T(Type an ordered pair.)

To get back to , rotate (1) about the origin, (0,0).T T

90°270°180°360°

-8 -4 4 8

xPQ

R

-8

-4

4

8y

-8 -4 4 8

x

-8

-4

4

8y

RQ

P

-8 -4 4 8

x

Q

-8

-4

4

8y

P

R

-8 -4 4 8

x

-8

-4

4

8y

PQ

R


33 of 61 2/26/16, 2:47 PM

77. Challenge Rotate rectangle PQRS about the origin, (0,0), to get rectangle . Then rotate rectangle about the origin, (0,0), to get rectangle

. What transformation can you perform on rectangle PQRS to get rectangle ?

270°P Q R S P Q R S 270°P Q R S P Q R S

Which of these shows rectangle ?P Q R S

A. B. C. D.

Which of these shows rectangle ?P Q R S

A. B. C. D.

What transformation can you perform on rectangle PQRS to get rectangle ?P Q R S

A. Reflect rectangle PQRS across the y-axis.B. Rotate rectangle PQRS 180 about the origin, (0,0).°C. Rotate rectangle PQRS 90 about the origin, (0,0).°D. Translate rectangle PQRS units up and units to the right.2 2E. Translate rectangle PQRS units down and units to the left.2 2F. Rotate rectangle PQRS 270 about the origin, (0,0).°G. Reflect rectangle PQRS across the x-axis.

-8 8

xQ

R

-8

8y

P

S

-8 8

x

R

-8

8y

P

Q

S-8 8

x

R

S

-8

8y

P

Q

-8 8

xQ

R

-8

8y

P

S

-8 8

xQ

R -8

8y

P

S

-8 8

x

R

S

-8

8y

P

Q

-8 8

xQ

R -8

8y

P

S

-8 8

xQ

R

-8

8y

P

S

-8 8

x

R

S

-8

8y

P

Q


34 of 61 2/26/16, 2:47 PM

78.

79.

80.

In the figure, || . Which angles are alternate interior angles?w hw

h

Choose the correct answer below. Select all that apply.

A. and ∠i ∠l B. and ∠u ∠i

C. and ∠u ∠v D. and ∠i ∠v

E. and ∠j ∠u F. and ∠j ∠k

Find the measure of v given that p||q.∠p

q

m v∠ = °

Streets A and B run parallel to each other. The measure of is . The measure of is . Find the measure of .

∠3 150°∠4 30° ∠6

m∠6 = °

i j

k l

uv

z

s

vx

rt u=99°

w=81°y

A St.

B St.

CSt.

1 2

3 4

5 6

7 8


35 of 61 2/26/16, 2:47 PM

81.

82.

83.

Writing Find the alternate interior angles in the figure shown given that m||n. Use pencil and paper. Describe a situation where you would use a transversal to cut a pair of parallel lines.

Which are the alternate interior angles. Select all that apply.

A. and ∠1 ∠7 B. and ∠2 ∠5

C. and ∠2 ∠7 D. and ∠3 ∠6

E. and ∠1 ∠8 F. and ∠3 ∠8

Rainbows When sunlight enters a drop of rain, different colors of light leave the drop at different angles, making a rainbow. In the figure shown, lines m and n represent thesun's rays. Assume that lines m and n are parallel and you are standing at the red dot. For violet light m 2 and m 3 . What is m 1? Use pencil and paper. Justify how you can determine m 1.

∠ = 26°∠ = 154° ∠

∠

m 1∠ = °

Find m given that p||q, m u , and m w .∠v ∠ = 75.8° ∠ = 104.2°p

q

m∠v =

12

34

56

78

m n

1

2

m

n

3

us

v wx

rt

y


36 of 61 2/26/16, 2:47 PM

84.

85.

86.

Think About the Process The figure shown represents lines being painted in a parking lot. Lines p, q, and r areparallel, m 1 is and m 2 is . Suppose you are painting the last line which is represented by the dashed line in the figure. To paint a parallel line, you need to angle your paint brush using m 4. How do you find m 4? Find m

∠ 33° ∠ 147°

∠ ∠ ∠

How do you find m 4?∠

A. All the lines are parallel, thus, m 4 m 1 because they are alternate interior angles.∠ = ∠B. All the lines are parallel, thus, m 4 m 2 because they are corresponding angles.∠ = ∠C. All the lines are parallel, thus, m 4 m 2 because they are alternate interior angles.∠ = ∠D. All the lines are parallel, thus, m 4 m 1 m 2.∠ = ∠ + ∠

m 4∠ = °

Challenge Engineers are laying pipe below ground on opposite sides of the street as shown here. To join the pipe, workers on each side of the street work towards the middle. One team of workers lays the pipe using m 4 . The other team of workers lays the pipe using m 2. Find m 2. Assume that the sides of the street are parallel and the pipe is straight.

∠ = 122°∠ ∠

m 2∠ = °

In the figure to the right, line m and line n are parallel. Determine whether the given angles are congruent or supplementary.

and ∠c ∠f m

n

Identify whether the pair of angles is congruent or supplementary.

anglessupplementaryanglescongruent

p

q

r

1 2

3 4

1 2

3 4

a bc d

e fg h


37 of 61 2/26/16, 2:47 PM

87.

88.

89.

90.

In the figure to the right, . Determine whether the given angles are congruent or supplementary.

m n

and ∠e ∠gm

n

Identify whether the pair of angles is congruent or supplementary.

anglessupplementaryanglescongruent

In the figure, and m 4 . Find the measures of the other angles.

m n ∠ = 126°

t

The measure of 6 .∠ = °







If and m e in the figure to the right, find the measures of a, c, and h.m n ∠ = 103°

∠ ∠ ∠m

n

m a (Type an integer or a decimal.)∠ = °

m c (Type an integer or a decimal.)∠ = °

m h (Type an integer or a decimal.)∠ = °

Find the value of x. Then find the measure of each labeled angle.

x° = °

(x )− 26 ° = °

x°

(x−26)°

a bc d

e fg h

45

36

m

81 2

7

n

a bc d

e fg h


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91. Find the measure of angles 1-7 given that lines m and n are parallel and t is transversal.

mn1

234

56

7

t

m ∠ 1 = o

m ∠ 2 = o

m ∠ 3 = o

m ∠ 4 = o

m ∠ 5 = o

m ∠ 6 = o

m ∠ 7 = o

49°


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92.

93.

Lines l1 and l2 are parallel lines. Determine the measures of

1 through 12.

7 = °

1 = °

2 = °

3 = °

4 = °

5 = °

6 = °

8 = °

9 = °

10 = °

11 = °

12 = °

(1) ECDAEDBECCED

DEB (2) DEBAEDBECCED

ECD

In the figure, is parallel to . m ECD , and m DEB . Find and m CDE.AB CD ∠ = 42° ∠ = 43° m ∠AEC ∠

C

Since AEC is congruent to (1) , then m AEC .∠ ∠ ∠ = °

Since CDE is congruent to (2) , then m CDE .∠ ∠ ∠ = °

59

62

D

EA B


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94.

95.

Draw the graph of triangle DEF after a dilation with center (0,0) and scale factor . 2


A. B. C.

Which of these graphs shows triangle , the image of after a dilation?Use pencil and paper. What types of transformations are shown in the other graphs?Explain.

D E F triangle DEF

Which graph shows the image after a dilation?

A. B. C.

0 5 10

x

5

0

5

10y

D E

F

90 18

x

9

0

18y

D E

F

60 10

x

D

E

F6

0

10y

60 12

x

6

0

12y

D E

F

50 10

x

5

0

10y

D E

F

90 18

xD

E

F

9

0

18y

60 12

xDE

F6

0

12y

60 12

x

DE

F

6

0

12y


41 of 61 2/26/16, 2:47 PM

96.

97.

Draw the graph of triangle PQR and triangle after a dilation with center (0,0) and scale factor .

P Q R3


A. B. C.

The coordinates of are ( , ), ( , ), and ( , ). Draw and the image of for the

dilation with center (0,0) and scale factor

triangle LMN L 1 3 M 5 7 N 5 5 triangle LMN triangle LMN

.12


A. B. C.

-10 -5 0

5

10

x

y

PQ

R

x

PQ

R

-9-19 0

10

18y

PQ

R

x

-4-8 0

4

0

8y

PQ

R

PQ

Q

x

-6-12 0

6

12y

PQ

R

PQ

R

40 8

x

4

0

8y

40 8

x

4

0

8y

40 8

x

4

0

8y


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98.

99.

has vertices , , and . Graph triangle KLM and triangle , its image after a dilation with center at K and scale factor .Triangle KLM K(1,3) L(6,7) M(6,5) K L M

2


A. B. C.

Photography A photographer uses a computer program to enlarge a photograph. When laid on a grid, the original photograph has coordinates , , , and . Graph rectangles PHOT and P'H'O'T', its image after a

dilation with center at the origin and scale factor .

P(0,0) H(6,0) O(6,9) T(0,9)83


A. B. C.

70 14

x

6

0

12y

70 14

x

6

0

12y

70 14

x

6

0

12y

100 20

x

14

0

28y

100 20

x

14

0

28y

100 20

x

14

0

28y


43 of 61 2/26/16, 2:47 PM

100.

101.

Think About the Process Quadrilateral EFGH has vertices , , , and . Using a scale factor

of , how can you find the coordinates of point G', the image of point G? Graph rectangles EFGH and E'F'G'H', its

image after a dilation with center at and scale factor .

E(4,4) F(16,4) G(16,12) H(4,12)54

E(4,4)54

How can you find the coordinates of point G'?

A. Multiply the coordinates of G by .4B. Multiply the coordinates of G by .5

C. Multiply the coordinates of G by .54

D. Add to the coordinates of G.54


A. B. C.

The coordinates of triangle PQR are P( , ), Q( , ), and R( , ). Graph triangle PQR and triangle , its image after a dilation with center (0,0) and scale factor . Use pencil and paper. Find the area of each triangle. What is the scale factor for the areas of the triangles?

3 − 3 3 5 4 − 3 P Q R2

Which graph below shows triangle PQR and the image ?triangle P Q R

A. B. C.

120 24

x

10

0

20y

120 24

x

10

0

20y

120 24

x

10

0

20y

6

x

P = P

Q

R

Q

R

0

-4

14y

8

x

P

Q

R

P

Q

R

0

-6

8y

10

x

P

Q

R

P

Q

R

0

-8

12y


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102.

103.

104.

Find the scale factor for the dilation shown.

The scale factor is .

(1)

Estimation Without doing calculations, use side DE and side D'E' to estimate the scale factor for the dilation shown. Then use two corresponding sides to find the scale factor.

Side D'E' looks about (1) times longer than side DE.

The scale factor for this dilation is .(Simplify your answer.)

1324

The blue figure is a dilation image of the black figure. The origin is the center of dilation. Tell whether the dilation is an enlargement or a reduction. Then find the scale factor of the dilation.

Is the dilation an enlargement or a reduction?

EnlargementReduction

The scale factor of the dilation is . (Simplify your answer.)

0 4 8 12 16 20 24

x4

8

12

16

20

24

y

D' E'

F'

DE

F

G'

G

0 2 4 6 8 10 12 14 16

x0

2

4

6

8

10

12

14

16y

E'

F'

E

F

D = D'

80 16

x

8

0

16y


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105.

106.

107.

For the dilation with center (0,0) shown on the graph, your friend says the scale factor is

. What is the correct scale factor? What mistake did your friend likely make?103

The correct scale factor is .(Type an integer or a fraction.)What mistake did your friend likely make?

A. Your friend found the ratio between non-corresponding sides.B. Your friend found the ratio between two sides of the original triangle.C. Your friend found the ratio between two sides of the image triangle.D. Your friend found the scale factor that enlarges to triangle A B C triangle ABC.

Estimation Without calculating, estimate the relationship between the larger figure and the smaller figure, its image after a dilation. Then find the scale factor.

Which statement best describes the two figures?

A. The two figures are the same size.B. The smaller figure is less than half the

size of the larger figure.

C. The smaller figure is more than half the size of the larger figure.

D. The smaller figure is about half the size of the larger figure.

The scale factor for this dilation is .(Simplify your answer.)

Challenge Find the scale factors for each of the dilations below. Use pencil and paper. Find the scale factor for the dilation from WXYZ to W''X''Y''Z''.

The dilation from WXYZ to W'X'Y'Z'The dilation from W'X'Y'Z' to W''X''Y''Z''

The dilation from WXYZ to W'X'Y'Z' has a scale factor of .

The dilation from W'X'Y'Z' to W''X''Y''Z'' has a scale factor of .

-10 10

x

-10

10yA

B

C

AB

C

0 2 4 6 8 10 12 14

xQ R

ST

Q R

ST

0

2

4

6

8

10

12y

8 16

x

11

0

22y

X'' X' X

Y''

Z''

Y'

Y

Z'

Z

W = W' = W''


46 of 61 2/26/16, 2:47 PM

108.

109.

110.

Triangle RST has vertices R( , ), S( , ), and T( , ). Triangle R'S'T' is the image of triangle RST after a dilation with

center (0,0) and scale factor . What are the coordinates of point '?

0 0 10 5 5 − 525

S

The coordinates of point ' are . S(Type an ordered pair.)

Rectangle QUAD has coordinates Q( , ), U( , ), A( , ), and D( , ). Q'U'A'D' is the image of QUAD after a dilation with center (0,0) and scale factor . What are the coordinates of point '?

5 3 5 6 10 6 10 32 Q

The coordinates of point ' are . (Type an ordered pair.)Q

Find the coordinates of ', the image of point after a dilation with center (0,0) and scale factor .

P P2

The coordinates of ' are . P(Type an ordered pair.)

-2 2 4 6 8

x

P

Q

R-2

2

4

6y


47 of 61 2/26/16, 2:47 PM

1. B. of .Triangle GHJ is a reflection triangle ABC

2. A.

3. A. Triangle A'B'C' is the image of triangle ABC after a reflection across the y-axis.

4. D. Triangle E'F'G' is the image of triangle EFG after a reflection across the x-axis.

5. C. Parallelogram of parallelogram ABCD.s EFGH and JKLM are reflections

6. D. The x-coordinates of the vertices are the same distance away from the y-axis but in the opposite direction.

A. The y-coordinates of the vertices are unchanged in the image.

D. Triangle A'B'C' is the image of triangle ABC after a reflection across the y-axis.

7. D. Triangle E'F'G' is the image of triangle EFG after a reflection across the line y = − 1.

B. Your friend took the reflection across the x-axis instead of the correct line of reflection.

8. (1) III

9. A. , C. The figure and the image are the same size. The figure and the image are the same shape.

A. A'B'C'D' is the image of ABCD after a reflection across the y-axis.

10. A. A'B'C'D' is the image of ABCD after a reflection across the line x .= 1

11. (1) y

4

12. (1) B

13. (1) C

14. C. 90°

-6 6

x

A

C

A'

C'

-6

6y

B B'


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15. C.

16. (1) C

17. A. 180°

18. (1) I.

C.

19. (1) B

20. C.

21. C.

A. 90°

-8 -4 4 8

xY

-8

-4

4

8y

X

Z

X

Y

Z

-8 -4 4 8

x

-8

-4

4

8y

T

R

I

T

R

I

-8 -4 4 8

xL

M M

N

-8

-4

4

8y

K

N

K

L

-8 8

x

-8

8y

TR

I

T

RI

O


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22. A.

23. A. , B. , D. 90° 450° 810°

24. B.

25. B.

26. ( − 1,7)

27. B.

28. A.

29. C. The x-coordinates by because " " indicates a change.decrease 4 left negative

(1,10)

-8 -4 4 8

xQ

R

-8

-4

4

8y

P

S

P

QR

S

0 2 4 6 8 10

x

D'

E'

F'

02

46

810

y

-10 0 10

xJ

K

L

10y

J'

K'

L'

-10 0 10

xG

R

10y

A

MG'

R' A'

M'

-5-10

x

5

10y

D'

E'

F'


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30. (1) ( − 6, − 6).

(2) ( − 4, − 7).

(3) ( − 5, − 3).

( − 7, − 5)

31. (1) III

32. A. , B. , C.The figure and the image are the same size. The figure and the image are the same shape.Each point in the image moves the same distance and direction from the figure.

B.

33. A.

34. B.

35. B.

B. It is a translation . The distance of the translation is twice the distance between L and M.to the left

M L

-10 10

x

G

R A

MG'

R' A'

M'-10

y

-10 10

xQ'

U' A'

D'

-10

10y

Q

U A

D

-10 -5 5 10

x

V W

XYZ

-10

-5

5

10y

V' W'

X'Y'Z'

Q


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36. A.

D. It is a rotation about the point C. The angle of rotation is clockwise.156°

37. D. The mapping is a glide reflection. The glide translation rule is (x,y) ( , ) and the reflection line is .→ x y + 4 x = 4

38. D. The mapping is a reflection. The reflection line is .x = − 512

39. A.

B. It is a translation . The distance of the translation is twice the distance between L and M.up and to the left

40. A.

C. It is a rotation about the point C. The angle of rotation is clockwise.124°

41. A.

B. It is a rotation about the origin. The angle of rotation is 180 .°

42. A.

78°

L

M

62°C

T

-6 6

xB

-6

6yA

A

B

-6 6

x

-6

6y

AB A

B


52 of 61 2/26/16, 2:47 PM

B. It is a translation up units.two

43. A. triangle trianglePCY ≅ XBN

44. B. triangle triangle WQZ ≅ CFA

B. T 5 , 3 ◦ r( )180°,O (triangle WQZ)

45. C. ≅GC FD

A. T 2 , − 6 ◦ Ry-axis GC

46. A. Yes. The congruence transformation is a reflection.

47. LKJ

48. S

T

U

ST

SU

TU

49. 34

34

50. 106

74

106

17

6

51. 5.7

27.2

27.2

52. 22

28

53. 4


53 of 61 2/26/16, 2:47 PM

5

6

DE

EF

FD

54. 4

5

6

WX

XY

YW

55. 4

6

5

RT

TS

SR

56. A.

57. B.

6,400

58. D. The image is up and to the right.

-5 5

x

-5

5y

0 120 240

x0

120

240y


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B.

59. ( − 2,0)

C.

60. − 2

2

61. C. (x,y) (x ,y )→ − 1 + 2

C. Your friend wrote a rule that describes the translation from the blue figure to the black figure.

62. A. (x,y) (x ,y )→ + 9 − 10

63. D. (x,y) (x ,y )→ + 1 + 12

C. (x,y) (x ,y )→ + 10 + 1

64. (4,4)

65. A.

-10 -5 5

x

-2

5

10y

-5 5

x

-5

5y

-10 10

x

-9

9y

A B

CD

A'B'

C' D'


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66. A.

67. (3, − 3)

68. B.

D.A reflection changes only a figure's position, not its size or shape. The image of the figure faces the opposite direction as the figure.

69. ( − 4, − 9)

70. B.

71. (3, − 2)

72. B.

73. ( − 2,5)

-7 7

xBB'

-7

7y

A

C

A'

C'

-10 10

x

JA

R

J'A'

R'-1

9y

-6 6

x

A''

C''

-6

6y

A

BC

B''

-8 -4 4 8

x

-8

-4

4

8y

P

Q

R


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B. rotated about the origin, (0,0).He N 270°

74. ( − 4, − 2)

75. ( − 2, − 3)

( − 6, − 4)

( − 2, − 6)

B.

76. ( − 5,4)

(1) 270°

77. B.

B.

B. Rotate rectangle PQRS 180 about the origin, (0,0).°

78. A. , F. and ∠i ∠l and ∠j ∠k

79. 99

80. 150

81. C. , D. and ∠2 ∠7 and ∠3 ∠6

-8 -4 4 8

x

-8

-4

4

8y

PQ

R

-8 8

x

R

S

-8

8y

P

Q

-8 8

xQ

R -8

8y

P

S


57 of 61 2/26/16, 2:47 PM

82. 26

83. 75.8

84. A. All the lines are parallel, thus, m 4 m 1 because they are alternate interior angles.∠ = ∠33

85. 58

86. anglescongruent

87. anglessupplementary

88. 126

126

126

54

54

54

54

89. 103

77

103

90. 103

77

91. 131

49

131

49

131

49

131

92. 59

59


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59

62

62

59

118

121

62

118

121

59

93. (1) ECD

42

(2) DEB

43

94. C.

95. A.

96. C.

60 12

x

6

0

12y

D E

F

90 18

xD

E

F

9

0

18y

x

-6-12 0

6

12y

PQ

R

PQ

R


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97. A.

98. A.

99. B.

100. C. Multiply the coordinates of G by .54

A.

101. C.

40 8

x

4

0

8y

70 14

x

6

0

12y

100 20

x

14

0

28y

120 24

x

10

0

20y

10

x

P

Q

R

P

Q

R

0

-8

12y


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102. 4

103. (1) 3

135

104. Reduction

13

105.310

D. Your friend found the scale factor that enlarges to triangle A B C triangle ABC.

106. B. The smaller figure is less than half the size of the larger figure.

12

107.1114

511

108. (4,2)

109. (10,6)

110. (8, − 2)


61 of 61 2/26/16, 2:47 PM

Butterflies, Pinwheels, and Wallpaper Unit Test Re …. 2. 3. Student: _ Date: _ Instructor:...

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Transcript of Butterflies, Pinwheels, and Wallpaper Unit Test Re …. 2. 3. Student: _ Date: _ Instructor:...

Butterflies, Pinwheels, and Wallpaper Unit Test Re …. 2. 3. Student: _____ Date: _____ Instructor:...

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Transcript of Butterflies, Pinwheels, and Wallpaper Unit Test Re …. 2. 3. Student: _____ Date: _____ Instructor:...

Butterflies, Pinwheels, and Wallpaper Unit Test Re …. 2. 3. Student: _ Date: _ Instructor:...

Transcript of Butterflies, Pinwheels, and Wallpaper Unit Test Re …. 2. 3. Student: _ Date: _ Instructor:...