UNIT 5: Transformations - WordPress.com · 05/05/2015 · Unit 5: Transformations Name: _____ 4...

Semester 2 Test Prep

UNIT 5: Transformations

Checklist

MAX Scored

1 Vocabulary 40

2 Transformations 30

3 Constructions 20

4 Random Transformations 30

Totals 120

Name: _______________________________

Period: __________ Date: May 11 & 12, 2015

Unit 5: Transformations Name: ___________________________

2 Semester 2 Test Prep

Section 1. Vocabulary

Word Bank (word is used only once; not all words will be used below)

Dilation Reflection Stretch / Shrink

Enlarges Rotation Translation

Isometric Transformation Shrinks Transformation

Df R30 rx-axis

Th,k

A ___________________ is an operation that maps or moves the points of a figure in a plane.

An ____________________________ is a transformation that keeps the size and shape of

the figure identical or congruent.

We examined three type of isometric transformations.

A ________________ moves, shifts or “slides” the figure in the coordinate plane.

A ________________ provides a mirror image of the figure by “flipping” the figure

against designated line.

A ________________ “turns” the figure about a fixed point.

Other types of transformations we’ve examined are not isometric:

A ______________ uses a scalar multiple to enlarge or shrink the figure. These

transformations are denoted by the form _______, with “F” being the multiplicative

factor. If F > 1, the image is _____________; if F < 1, the image ____________.

Of note, a dilation changes the lengths of a shape, but retains congruent angles.



A ___________________ multiplies the planar coordinates by different scalar factors.

These transformations are denoted by the form Sa,b with “a” being the “x” multiplier and “b”

being the “y” multiplier. Of note, if a 1 and b 1, the image will have no congruent sides or

angles.

T F 1 When working with multiple transformation, order matters. If you

change the order of the multiple transformations, you will typically get a

different image.

2 When working with multiple transformations, you work the order “inside-

out”, meaning you start with the most inner transformation, then work

toward the outside.

3 Th,k (R90(x,y)) = R90 (Th,k (x,y))

4 R180 (x,y) = rx=y (rx=-y(x,y))

Fill in the transformation mappings:

Translation Reflection Rotation

Th,k = (x+h, y+k) rx-axis (x,y) = ( , )

ry-axis (x,y) = ( , )

rx=y (x,y) = ( , )

The rotations about the

origin (0,0):

R90 (x,y) = ( , )

R180 (x,y) = ( , )

R270 (x,y) = ( , )



Match the definition to the key word.

a. ___ Point

A. Identical in form and measurement

B. A set of collinear points with two

reference points.

C. Lines that have equal slopes but different

y-intercepts.

D. A set of points which are all the same

distance from a certain point.

E. An exact position or location in a plane.

F. An angle that measures exactly 90

G. Part of a line with two end points

H. A figure formed by two rays with a

common endpoint

I. Lines that have slopes that are opposite

sign reciprocals

J. A parallelogram with 4 congruent sides.

K. A parallelogram with 4 right angles

L. A parallelogram with 4 right angles AND 4

congruent sides

M. A line that cuts across two or more

parallel lines

N. The point that divides a line segment into

exactly two equal parts

b. ___ Rhombus

c. ___ Angle

d. ___ Line Segment

e. ___ A rectangle

f. ___ Midpoint

g. ___ Circle

h. ___ Right Angle

i. ___ Congruent

j. ___ Line

k. ___ A square

l. ___ Perpendicular Lines

m. ___ Parallel Lines

n. ___ Transversal line



Section 2. Transformations

A. T3,-3 (7,3) =

B. rx-axis (-8,5) =

C. T2,3 (R180 (-5,2)) =

D. R180 (T2,3 (-5,2)) =

E. rx=y (R270 (-3,-4)) =

F. D4 (-5,3) =

G. R90 (-3,-5) =

H. rx=1 (4,-2) =

I. ry=-1 (2,18) =

J. rx=-y (-4, 1) =

K. If g(x,y) = (5, -8) and f(x,y) = (2x+1, -3y-2), then f(g(x,y)) =

L. If A = (-3,9), then rx-axis (R180 (A)) =

M. Given P(-3,6) and T(x-4,y+2), P’’ after a reflection over the y-axis of

the point T(P) . . . .

N. What is point A” if A(-3,7) has undergone ( ) 7, 2(T (A))?x axisr



Section 3. Constructions

A. Draw an image with one line of symmetry.

B. Draw an image with three lines of symmetry.

C. Draw an image with an infinite number of lines of symmetry.

D.



E. Which of the following is the definition of a circle?

a) A figure without any corners

b) A figure with an infinite number of parallel lines of equal length

c) The resulting figure when a rounded cone is cut obliquely (look up the word) by a

plane.

d) The set of all points that are the same distance from a point called a center.

F. Describe every transformation that maps a square with points (2,2), (-2,2), (-2,-2) and

(2,-2) onto itself. Hint: there are at least 5 transformations.

G.

Hint: Start with the graph



Section 4. Random Transformations

A. Find the coordinates of the vertices of R180 (T-3,8 (ABC) where A (2,3), B (6,7) and C (9,4).

Hint: Use a table!!!!!!!!

B. Given the figure below, ABC, what would be the coordinates under R180 (T3,-2 (ABC)

Hint: Use a table or a graph!

Initial

A (1,4)

B (6,3)

C (3,1)

C.



D.

E.



F. G.



H.

I.



J.

K.



KEY



Section 1. Vocabulary (One point each response)

A ______________________ is an operation that maps or moves the points of a figure in a

plane. An ___________________________________ is a transformation that keeps the

size and shape of the figure identical or congruent.

We examined three type of isometric transformations.

A ________________ moves, shifts or “slides” the figure in the coordinate plane.

A _______________ provides a mirror image of the figure by “flipping” the figure

against designated line.

A ______________ “turns” the figure about a fixed point.

Other types of transformations we’ve examined are not isometric:

A ______________ uses a scalar multiple to enlarge or shrink the figure. These

transformations are denoted by the form _______, with “F” being the multiplicative

factor. If F > 1, the image is _____________; if F < 1, the image ____________.

Of note, a dilation changes the lengths of a shape, but retains congruent angles.

A ___________________ multiplies the planar coordinates by different scalar factors.

These transformations are denoted by the form Sa,b with “a” being the “x” multiplier and

“b” being the “y” multiplier. Of note, if a 1 and b 1, the image will have no congruent

sides or angles.

KEY

TRANSFORMATION

ISOMETRIC TRANSFORMATION

TRANSLATION

REFLECTION

ROTATION

DILATION

ENLARGED SHRINKS

STRETCH / SHRINK

DF



T F 1 When working with multiple transformation, order matters. If you

change the order of the multiple transformations, you will typically get a

different image. T

2 When working with multiple transformations, you work the order “inside-

out”, meaning you start with the most inner transformation, then work

toward the outside. T

3 Th,k (R90(x,y)) = R90 (Th,k (x,y)). Order matters. F

4 R180 (x,y) = rx=y (rx=-y(x,y)) T

Translation Reflection Rotation

Th,k = (x+h, y+k) rx-axis (x,y) = ( x , -y )

ry-axis (x,y) = ( -x , y )

rx=y (x,y) = ( y , x )

R90 (x,y) = ( -y , x )

R180 (x,y) = ( -x , -y )

R270 (x,y) = ( y , -x )



a. E Point

A. Identical in form and measurement

B. A set of collinear points with two reference

points.

C. Lines that have equal slopes but different

y-intercepts.

D. A set of points which are all the same

distance from a certain point.

E. An exact position or location in a plane.

F. An angle that measures exactly 90

G. Part of a line with two end points

H. A figure formed by two rays with a common

endpoint

I. Lines that have slopes that are opposite sign

reciprocals

J. A parallelogram with 4 congruent sides.

K. A parallelogram with 4 right angles

L. A parallelogram with 4 right angles AND 4

congruent sides

M. A line that cuts across two or more parallel

lines

N. The point that divides a line segment into

exactly two equal parts

b. J Rhombus

c. H Angle

d. G Line Segment

e. K A rectangle

f. N Midpoint

g. D Circle

h. F Right Angle

i. A Congruent

j. B Line

k. L A square

l. I Perpendicular Lines

m. C Parallel Lines

n. M Transversal



Section 2. Transformations (One point each response)

Translation: Reflections: Rotations: Dilation:

A. T3,-3 (7,3) = (10,0)

B. rx-axis (-8,5) = (-8,-5)

C. T2,3 (R180 (-5,2)) = (7,1)

D. R180 (T2,3 (-5,2)) = (3,-5)

E. rx=y (R270 (-3,-4)) = (3,-4)

F. D4 (-5,3) = (-20, 12)

G. R90 (-3,-5) = (5,-3)

H. rx=1 (4,-2) = (-2,-2) . . . draw diagram

I. ry=-1 (2,18) = (2,-20) . . . draw diagram

J. rx=-y (-4, 1) = (-1, 4) . . . draw diagram

K. If g(x,y) = (5, -8) and f(x,y) = (2x+1, -3y-2), then f(g(x,y)) = (11,22)

L. If A = (-3,9), then rx-axis (R180 (A)) = (3, 9)

M. Given P(-3,6) and T(x-4,y+2), P’’ after a reflection over the y-axis of the point

T(P) . . . . P” = (7,8)

N. What is point A” if A(-3,7) has undergone ( ) 7, 2(T (A))?x axisr

A” = (4, -5).

( , ) ( , )

r ( , ) ( , )

r ( , ) ( x, y)

x axis

y x

y axis

r x y x y

x y y x

x y

90

180

270

( , ) ( , )

( , ) ( , )

( , ) ( , )

R x y y x

R x y x y

R x y y x

, ( , ) ( , )h kT x y x h y k DF (x,y) = (Fx, Fy)



Section 3: Constructions

A. Draw an image with one line of symmetry.

B. Draw an image with three lines of symmetry.

Equilateral Triangle

C. Draw an image with an infinite number of lines of symmetry.

A circle

D.

a.

A reflection about the line y = -1

A rotation of 360 about (2, -1)

b.

A reflection about y = 1

A reflection about x = -2

A rotation of 180 about (-2, 1)

A rotation of 360 about (-2, 1)

E. Definition of a circle: Answer: (d)



F. Transformations of a square onto itself:

R90. Technically, any rotation that is a whole-number multiple of 900 works.

r x-axis

r y-axis

r y = x

r y = -x

G. Transformation of a hexagon

Mapping onto itself (minimums):

Rotation R60 (or whole

number multiples of 60)

rx-axis

ry-axis

ry=-1.73x

ry=1.73x

ry=-0.58x

ry=0.58x



Section 4: Various transformations

A. Find the coordinates of the vertices of R270 (T-3,8 (ABC) where A (2,3), B (6,7) and C (9,4).

Initial T-3,8 R270

A (2,3) (-1,11) (11,1)

B (6,7) (3,15) (15,-3)

C (9,4) (6,12) (12,-6)

B. Given the figure below, ABC, what would be the coordinates under R180 (T3,-2 (ABC)

Initial T3,-2 R180

A (1,4) (4,2) (-4,-2)

B (6,3) (9,1) (-9,-1)

C (3,1) (6,-1) (-6,1)

C.



D. a. Rotate ABCD by R-90 on Point (0,0), then Translation: T0,-3 (note: R-90 R270)

b. Reflection of ABCD on y = 1, then Translation: T6,0

E. Answer: Selection C.

F. Answer: Selection B (a “flip” or reflection on the y-axis)

G. Answer: Selection C.

A: (x,y) (-x,y) (x,-y) (-x,-y). NO

B: (x,y) (x,-y) (-x,-y) (-x,y). NO

C. (x,y) (-x,y) (-x,-y) (x,y). YES

D. (x,y) (x,-y) (-x,-y) (-y, x) NO

H. Answer: Selection B.

I. Answer: Selection C. A classic rotation of R270 (x,y) (y, -x)

J. Answer: Selection A.

Picking Point M (5,1) to M’(-9,-1)

A: (5,1) (-5,1) (-9,1) (-9,-1). YES

B: (5,1) (-5,-1) (5,-1) (7,-1). NO

C: (5,1) (1,1) (1,-1) (-1,-1). NO

D: (5,1) (1, -5) (1, 5) (5, -1)

K. Answer: Selection C. T12, -2

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