Transformation #3: Rotations NB Page...

Transformation#3:Rotations NBPage8

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ROTATIONNOTES:Arotationisatransformationwhich_______________________thefigureabouta________________________.

Thispointiscalledthe_____________________________________________;formostrotationsitwillbethe

__________________________butitcanbeotherpointstoo.Positiverotationsalwaysturn

______________________________________.

HW3)

Chooseyourownrotationfromoneofthese90,180,270degrees.

Writethisrotationasamapping/rule.

ℜ___ : (x, y) → (x ______, y ______)

Pick3points

X(___,___)Y(____,____)Z(____,____).Andgraphthem

Find

X’(___,___)Y’(____,____)Z’(____,____).Andgraphthem

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What are the coordinates of:

A ________! A’ _________

B ________! B’ _________

C ________! C’__________

Write a general rule for a y=x reflection:(x, y) ! ( ________ , _______ ).

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4)Rotatethetriangle270degreesabouttheorigin


6) Identify a rule and write the notation for each of the above

7) Rotate quadrilateral KLMN 90 degrees clockwise about point M to create its image. Find the coordinates of the new points.

! "#$!%9!/_*13,/+&!Triangle ABC is labeled on your graph below.

a) Rotate Triangle ABC, 90o counterclockwise. Label the

triangle A! B! C!.

b) Rotate Triangle ABC, 180o counterclockwise. Label the

triangle A" B" C".

c) Rotate Triangle ABC, 270o counterclockwise. Label the

triangle A!!! B!!! C!!!.

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Points: Line: Slope:




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units up. Draw the image !A’B’C’. What are the coordinates of: A (1, -3) ! A’ _________ B (3, 0) ! B’ _________ C (4, -2) ! C’__________

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L’’ ( ____, ____)

M’’ (____, ____)

N’’ (____, ____)

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●29 On a coordinate grid, triangle PQR is translated 4 units up and then reflected over the y-axis to form triangle P′Q′R′.

Which diagram could show triangle PQR, and the location of triangle P′Q′R′ after the transformations?

A.

1 2 3 4 5 6–1–2–3–4–5–6

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0

y

x

R R'

QP

Q'P'

B.

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y

xP

R

Q'

P'

R' Q

C.

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xP

R Q'

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D.

1 2 3 4 5 6–1–2–3–4–5–6

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xP

RQ'

P'

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●22 The diagram below shows !HIJand its image ! ′ ′ ′H I J after a single transformation.

y

x–5–6 –3 –2–4 3 54 6

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–3

–1

–6

–4

–2

21–1 0

1

3

5

2

4

6

H '

J 'I '

H

JI

Which of the following describes the transformation?

A. refl ection over the x-axis

B. refl ection over the y-axis

C. rotation 90° clockwise about the origin

D. rotation 180° clockwise about the origin


y

x–5–6 –3 –2–4 3 54 6

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●42 Quadrilateral KLMN is shown on the coordinate grid below.

–1

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–4–5–6–7–8–9

–9 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9

y

x0

(–6, –2)KL(–2, –3)

(–3, –6)M(–7, –5)N

Copy the coordinate grid and quadrilateral KLMN exactly as shown onto the grid in your Student Answer Booklet.

Quadrilateral KLMN will be translated 9 units up.

a. On your grid, draw quadrilateral ′ ′ ′ ′K L M N , the image of quadrilateral KLMN after it has been translated 9 units up. Be sure to label the vertices.

Quadrilateral ′ ′ ′ ′K L M N will be reflected over the y-axis.

b. On your grid, draw quadrilateral ′′ ′′ ′′ ′′K L M N , the image of quadrilateral ′ ′ ′ ′K L M N after it has been reflected over the y-axis. Be sure to label the vertices.

c. Explain whether a 180° rotation of quadrilateral KLMN about the origin would result in vertices with the same coordinates as ′′ ′′ ′′ ′′K L M N .

Quadrilateral ′′ ′′ ′′ ′′K L M N will be rotated 90° clockwise about point ′′M to create quadrilateral K L M N″′ ″′ ″′ ″′.

d. What are the coordinates of point ′′′K ?

ROTATIONASSIGNMENT:

HW1)Draw the final image created by rotating triangle RST 90° counterclockwise about the origin.

b) What are the coordinates of (- 5, 4) under a 180° counterclockwise rotation about the origin? c)What are the coordinates of ( 3, 2) under a 90° clockwise rotation about the origin?

HW2)PointP(6,7)andPointQ(6,4)areplottedonthecoordinategridbelow.



3) Identify a rule and write the notation for each of the above

!"#$!%7!).(*(-."!*++-2"1/"(&!1) Describe how you could move shape 1 to exactly match shape 1’ by using series of transformations?

2) Determine the transformation that produced the following image:

3) Draw the final image created by rotating triangle RST 90° counterclockwise about the origin !

4) What are the coordinates of (- 5, 4) under a 180° counterclockwise rotation about the origin? 5) What are the coordinates of ( 3, 2) under a 90° clockwise rotation about the origin?

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●13 Point P(6, 7) and point Q(6, 4) are plotted on the coordinate grid below.

Q

P

0 1 2 3 4 5 6 7 8 9 10

123456789

10

y

x

Point P is rotated 180° clockwise about point Q. What are the coordinates of the image of point P after this rotation?

A. (3, 4)

B. (6, 1)

C. (6, 10)

D. (9, 4) ●34 The diagram below shows XY and its

image X Y′ ′ after a single transformation.

–1

123456789

–2

–9 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9

y

x0

Y(–8, 5)

X(–2, 3)

Y' (8, 5)

X' (2, 3)


A. rotation 90° clockwise about the origin

B. translation 4 units to the right

C. refl ection over the x-axis

D. refl ection over the y-axis


–1

123456789

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–9 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9

y

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●13 Point P(6, 7) and point Q(6, 4) are plotted on the coordinate grid below.

Q

P

0 1 2 3 4 5 6 7 8 9 10

123456789

10

y

x

Point P is rotated 180° clockwise about point Q. What are the coordinates of the image of point P after this rotation?

A. (3, 4)

B. (6, 1)

C. (6, 10)

D. (9, 4) ●34 The diagram below shows XY and its

image X Y′ ′ after a single transformation.

–1

123456789

–2

–9 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9

y

x0

Y(–8, 5)

X(–2, 3)

Y' (8, 5)

X' (2, 3)


A. rotation 90° clockwise about the origin

B. translation 4 units to the right

C. refl ection over the x-axis

D. refl ection over the y-axis


–1

123456789

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y

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Transformation #3: Rotations NB Page...

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Transcript of Transformation #3: Rotations NB Page...