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Page Topic Resource4 Sample Pacing Guide

5-6 Ideas for Implementation and Helpful Hints

7-15 Binder Covers, Dividers and Spine Labels

17-18 Basics of Transformations Student Handout 1

19 - 20 Basics of Transformations Homework 1

21-22 Translations on the Coordinate Plane Student Handout 2

23-24 Translations on the Coordinate Plane Homework 2

25-26 Reflections on the Coordinate Plane Student Handout 3

27 Reflections on the Coordinate Plane Homework 3

29-30 Rotations on the Coordinate Plane Student Handout 4

31 Rotations on the Coordinate Plane Homework 4

33-34 Identifying Transformations Student Handout 5

35 Identifying Transformations Homework 5

37-38 Quiz: Translations, Reflections and Rotations Quiz 1

39-40 Scale Factor and Dilations Student Handout 6

41 Scale Factor and Dilations Homework 6

43-44 Dilations on the Coordinate Plane Student Handout 7

45-46 Dilations on the Coordinate Plane Homework 7

47-48 Properties of Transformations Student Handout 8

49-52 Transformations Study Guide—CCSS Review—CCSS

53-56 Transformations Study Guide Review

57-59 Transformations Unit Test Test

Transformations UnitTable of Contents

©Maneuvering the Middle LLC, 2016


Transformations UNITPACING GU IDE

DAY 1 DAY 2 DAY 3 DAY 4 DAY 5Basics of

TransformationsTranslations on the Coordinate Plane

Reflections on the Coordinate Plane

Rotations on the Coordinate Plane

Identifying Transformations

Student Handout 1Homework 1





DAY 6 DAY 7 DAY 8 DAY 9 DAY 10Translations,

Reflections and Rotations Quiz

Scale Factor and Dilations

Dilations on the Coordinate Plane

Properties of Transformations

Transformations Study Guide

Quiz 1 Student Handout 6Homework 6


Student Handout 8 Study Guide

Day 11 notesTransformations

Unit Test

Test

TRANSFORMATIONS


Student Handouts*NOTE: This file has been organized for double-sided printing. Any blank pages were left so intentionally to make printing easy.

Ideas for Implementation: This bundle has all of the notes, homework, quizzes, and tests to make your life easier and help your students to be successful with transformations. A sample pacing guide is included for those of you who do not have a district scope and sequence or if it is very general. Additionally, an answer key is included.

If you notice any discrepancies in the documents or have any questions, please email me at: [email protected].

standards8.G.1 Verify experimentally the properties of rotations, reflections and translations;a. Lines are taken to lines, and line segments to line segments of the same length.b. Angles are taken to angles of the same measure.c. Parallel lines are taken to parallel lines.

8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

mailto:[email protected]

HELPFUL Hints

A few ideas for organizing your curriculum and keeping things nice and neat.

Keep each unit in a separate binder. Use the spine labels and covers to keep them looking nice and easy to find. I personally love 1.5 inch binders.


Student Handouts

BINDERS

I place my originals in page protectors in chronological order. I hole punch any extra copies from that lesson and place them behind that page. When I need an extra or a student is missing something from weeeeeeeeks ago, I can simply pull a copy out.

Page protectors

I highlight the edges of my answer keys, or, if I am really good, I print them on colored paper. This helps them to stand out and makes them easy to find on my desk, in a binder, by the document camera, etc. Plus, highlighter doesn’t show up if you make a copy.

Answer Keys

Cardstock in a page protector makes an awesome divider. When I set up my dividers, I include one for each of the following: handouts, activities, assessments, and answer keys. Binder covers and spine labels have been included.

Cardstock

Happy Teaching!

E i g h t h G r a d e C u r r i c u l u m

U n i t s e v e n

8 . g . 1 8 . g . 2 8 . g . 3 8 . g . 4

©MANEUVERING THE MIDDLE, 2016

transformations

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U n i t s e v e n : A n s w e r K e y


transformations



U n i t s e v e n : a c t i v i t i e s

transformations



U n i t s e v e n : a s s e s s m e n t s

transformations

_____________________

KEYWORDS:

_____________________

KEYWORDS:

_____________________

KEYWORDS:

_____________________

KEYWORDS:

GEOMETRIC TRANSFORMATIONS

• To transform a shape or figure means to _____________ it. In general,

we can change the size, location and direction that a figure is facing.

• The shape or figure before the transformation is called the _____-

___________, or original. We might label it A.

• The shape or figure after the transformation is called the __________,

or new figure. We would then label it A’, pronounced “A ____________”.

Complete the following which gives an overview of the types of transformations we’ll cover this unit.

Unit: TransformationsStudent Handout 1


Name _____________________________________Date _____________________________Pd______

A

A’

B B’

d

D’

C

C’

Where do you see transformations in the real world? List some examples below.

Translations: Reflections: Rotations: Dilations:

Basics of transformations

CONGRUENCE & ORIENTATION

• Congruence refers to whether or not a figure has the same ________ and

__________ after a transformation.

• Orientation of the ______________ refers to whether or not the figure is

facing the same direction on the coordinate plane after a transformation.

• Orientation of the ______________ refers to the order in which the vertices

are labeled, clockwise or counterclockwise.

1. Transformation: _________________________

Size: ______________

Orientation of Figure: ______________

Orientation of Vertices: ______________

2. Transformation: _________________________

Size: ______________



3. Transformation: _________________________

Size: ______________



4. Transformation: _________________________

Size: ______________



Summarize today’s lesson:

Label the type of transformation shown. Then, state whether the size and orientation changed or stayed the same.

a

B

c C’

B’

A’ a

B

c A’

B’

C’

a

B

c A’

B’

C’ a

B

cB’

A’C’


Unit: TransformationsHomework 1

Name _____________________________________Date _____________________________Pd______

1. Use the graph to determine which transformation is shown by the following figures:

a. Figure A and Figure B: _____________________

b. Figure B and Figure C: _____________________

c. Figure C and Figure D: _____________________

d. Figure D and Figure E: _____________________

2. Which of the following describes how you can tell which figure in a transformation is the original figure?

A. It is always the figure on the left.B. It is always the larger figure.C. It is always the figure with “prime” notations.D. It is always the figure without “prime”

notations.

3. Which of the following is a true statement about a dilation?

A. It changes the size of a figure.B. It changes the orientation of a figure.C. It changes the orientation of the vertices.D. All of the above are true.

4. Mrs. Hannigan rearranged a couch in her living room as shown. Mark each statement as true or false.

5. Fill in the statements below with “sometimes”, “always” or “never” in order to make them true.

a. A reflection will ______________________ change the orientation of a figure.

b. A reflection will ______________________ change the size of a figure.

c. A reflection will ______________________ change the orientation of the vertices of the figure.

A b

c

d e

couch

a b

D C

couch

A’

b’c’

d’ ________a. Mrs. Hannigan reflected the couch.

________b. Mrs. Hannigan changed the orientation of the figure.

________c. Mrs. Hannigan changed the orientation of the vertices.


Basics of transformations

6. The graph below shows a rotation. Graham thinks that the shape was rotated from Quadrant I to Quadrant IV. Is he correct? Why or why not?

7. The graph below shows a dilation. Shelley says that the original image was enlarged, but Steve thinks the original image was reduced. Who is correct?

A

A’.A .A’

Type of transformation size of figure orientation of figure orientation of vertices

Translation

Reflection

Rotation

Dilation

8. Complete the table by writing “same” or “changed” for each type of transformation.


1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8

1. Translate the figure 5 units left and 2 units down. Record the coordinates of the pre-image and image in the table.

Look for any patterns and describe what happened to the x and y values in each ordered pair:

How can we represent this algebraically?

2. Translate the figure 4 units right and 3 units up. Record the coordinates of the pre-image and image in the table.

Look for any patterns and describe what happened to the x and y values in each ordered pair:

How can we represent this algebraically?

TRANSLATIONS

• A translation moves every point of a figure the same ________________ and

the same ________________.

• A translation can move a figure _______________ and/or _____________ .

• Translations are also thought of as ________________.


Name _____________________________________Date _____________________________Pd______

Pre-Image Image

A (2, 4) A’(-3, 2)

B(6, 7) B’(1, 5)

C(7, 3) C’(2, 1)

Pre-Image Image

D(-7, -4) D’(-3, -1)

E(-4, 1) E’(0, 4)

F(-3, -5) F’(1, -2)

A

B

C

D

E

F


●

●

●

●

●●

TRANSLATIONS ON THE COORDINATE PLANE

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8

3. Record the coordinates of the pre-image and image in the table below.

Verbal description of the translation:

Algebraic representation of the translation:

What do you notice about the line segments in the pre-image and image? Do they change size?

4. Record the coordinates of the pre-image and image in the table.

Verbal description of the translation:

Algebraic representation of the translation:

What do you notice about the angle measures in the pre-image and image? Do they change size?

5. Describe the translation:

M (12, 7) M’ (-1, 14)


n (-6, -8) n’ (-5, 2)


o (-3, 6) o’ (-9, -1)

Pre-Image Image

G(2, -7) G’(-5, -3)

H(2, -1) H’(-5, 3)

I(5, -1) I’(-2, 3)

J(5, -7) J’(-2, -3)

Pre-Image Image

K(-7, 2) K’(2, -7)

L(-2, 2) L’(7, -7)

M(-2, 7) M’(7, -2)

N(-7, 7) N’(2, -2)

· ···

··G’

H’ I’

G

h

I

·j’·

j

·· ·

·· ·k’

m’

L’

n’·k

m

L

·n


1. Describe, in words, how the figure at the right was translated.(Include how many units and which direction.)

2. Represent the translation algebraically:

3. Use the translation below to label the following statements as true or false.

4. Figure XYZ was translated as shown in the table of coordinates below.

Give an algebraic representation for the translation.

_______________

5. The coordinates for triangle PQR are shown in the table below.

Find the coordinates of the image after a translation 7 units to the left and 6 units up. Record the coordinates in the table.


Name _____________________________________Date _____________________________Pd______

_____a) The figure was translated from Quadrant I to III.

_____b) The translation can be represented by (x + 8, y + 7).

_____c) The orientation of the figure did not change.

_____d) The image and the pre-image are congruent.

_____e) The orientation of the vertices changed.

Pre-Image Image

X (-3, 9) X’ (6, 5)

Y (-6, 10) Y’ (3, 6)

Z (-1, 4) Z’ (8, 0)

Pre-Image Image

P (12, 3)

Q (14, 6)

R (8, 4)


1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8

A’

A

A

bc

B’C’

a’

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8

TRANSLATIONS ON THE COORDINATE PLANE

6. Translate the figure 9 units right and 9 units up. Be sure to label your vertices.

7. The figure below is going to be translated 7 units left and 9 units up. In which quadrant will the image lie?

___________________

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8

Coordinates Description Algebraic representation

8. T (-4, 7) T’ (-11, 14)

9. U (3, -9) U’ (10, -16)

10. V (-2, -10) V’ (5, -3)

7 units right, 7 units up

7 units left, 7 units up

7 units right, 7 units down

(x – 7, y + 7)

(x + 7, y + 7)

(x + 7, y – 7)

The coordinates below represent points that were translated. Draw a line to connect the coordinates with the correct description and algebraic representation of the translation.

e f

gh


● ●

●●

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8

1. Reflect the figure shown over the y-axis. Record thecoordinates of the pre-image and image.

How can we represent this algebraically? ____________

2. Reflect the figure shown over the x-axis. Record thecoordinates of the pre-image and image.

How can we represent this algebraically? ____________

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8

REFLECTIONS

• A reflection ___________ a figure over a line of __________________ in

order to create a __________ image.

• Each reflected point of the figure should be the same distance from the

line of ___________________ on the opposite side.


Name _____________________________________Date _____________________________Pd______

Pre-Image Image

W(2, 6) W’(-2, 6)

X(7, 4) X’(-7, 4)

Y(2, 2) Y’(-2, 2)

Describe any patterns found in the ordered pairs:

Pre-Image Image

D(2, -2) D’(2, 2)

E(7, -7) E’(7, 7)

F(2, -7) F’(2, 7)

Describe any patterns found in the ordered pairs:

w

x

y

d

ef

Highlight and identify the line of reflection in each of the examples:


●

●●

●

●

●

REFLECTIONS ON THE COORDINATE PLANE

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8

5. Bella thinks that the transformation below represents a translation. Is she correct? Why or why not?

6. Use the chart to compare and contrast translations and reflections.

7. Use what you’ve learned to show where the following points would be after the given reflections:

8. Write in your own words what happens to the coordinates in a figure when the following occur:

• Reflection over the x-axis:

• Reflection over the y-axis:

3. Reflect triangle PQR over the y-axis. Then, describe what happened to each of the coordinates.

4. Reflect your new triangle P’Q’R’ over the x-axis. Then, describe what happened to each of the coordinates. p

q

r

Similarities DIFFERENCES

g

h i

j J’

I’ H’

G’

Pre-imageReflection

over x-axisReflection over y-axis

A(6, 8)

B(-5, 1)

C(10, -9)

D(-4, -11)

E(7, 12)



1. Point D (9, -8) isreflected to D’ (9, 8).

____________________

2. A figure is reflected from Quadrant II to Quadrant III.

____________________

3.

____________________

4. Point T (-7, -1) is reflected to T’ (7, -1).

____________________

5. A figure is reflected from Quadrant I to Quadrant II.

____________________

6.

____________________

7. Point E (11, 6) is reflected to E’ (11, -6).

____________________

8. A figure is reflected from Quadrant IV to Quadrant III.

____________________

9. Reflect the figure shown over the y-axis. Record the coordinates of the image.

M’ ________ A’________ T’________ H’________

10. Reflect the figure shown over the x-axis. Record the coordinates of the image.

J’________ K’________ L’________

11. Using the reflection in #9, describe what happened to each of the following by writing “same” or “changed”.

a. Size of the figure: _______________

b. Orientation of the figure: _______________

c. Orientation of the vertices: _______________

12. Using the reflection in #10, describe what happened to each of the following by writing “same” or “changed”.

a. Size of the figure: _______________

b. Orientation of the figure: _______________

c. Orientation of the vertices: _______________


Name _____________________________________Date _____________________________Pd______

For questions1-8, identify the line of reflection by writing “x-axis” or “y-axis”.


1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8

m

a t

h

●

● ●

●

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8L

K

J

●

●●

REFLECTIONS ON THE COORDINATE PLANE

1.

________ clockwise

_________counterclockwise

2.

________ clockwise


3.

________ clockwise


4.

________ clockwise


5.

________ clockwise


6.

________ clockwise


ROTATIONS

• A rotation ____________ a figure around a fixed point called the center of

________________.

• For our examples, the center of rotation will be the _____________, and we’ll

rotate in increments of ________.

DIRECTIONS AND DEGREES

Pay attention to the direction of the rotation!

Consider each quadrant as another 90°in the rotation.


Name _____________________________________Date _____________________________Pd______

B

A

A’C

C’

DD’

E

E’

F

F’

Find the number of degrees in each rotation shown below.


Rotations on the coordinate plane

7. Rotate the figure shown at the right 90°, then 180°, and then 270° clockwise. After each rotation, record the coordinates of the image in the appropriate table.

Look for any patterns to try and create the algebraic representation for each rotation.

90° Clockwise(270° counterclockwise)

A (2, 1)

B (6, 1)

C (4, 7)

Algebraic representation:

In your own words:


A (2, 1)

B (6, 1)

C (4, 7)


In your own words:


A (2, 1)

B (6, 1)

C (4, 7)


In your own words:

· ··

A b

c

The coordinates below represent rotations. Use what you’ve learned today to describe what type of rotation occurred.

8. X (9, 8) X’ (8, -9) _____________________________________________________________________

9. Y (-4, 5) Y’ (-5, -4) ___________________________________________________________________

10. Z (-6, -1) Z’ (6, 1) ____________________________________________________________________

11. Do rotations preserve or change the orientation of the figure?


12. Do rotations preserve or change the orientation of the vertices?



Name _____________________________________Date _____________________________Pd______

Use the figure to answer the questions below. Match your answers in the table to solve the riddle.

1. Find A’ after A is rotated 90° clockwise.

2. Find B’ after B is rotated 270°clockwise.

3. Find C’ after C is rotated 180°clockwise.

4. Find D’ after D is rotated 90° clockwise.

5. Find A’ after A is rotated 180°counterclockwise.

6. Find B’ after B is rotated 270°counterclockwise.

7. Find C’ after C is rotated 90°counterclockwise.

8. Find D’ after D is rotated 180°counterclockwise.

9. Find A’ after A is rotated 270°clockwise.

10. Find B’ after B is rotated 180°clockwise.

11. Find C’ after C is rotated 90° clockwise.

12. Find D’ after D is rotated 90°counterclockwise.

S (7, -7) L (1, -7) C (-2, -7)

B (-7, -7) O (-7, -1) W (2, 1)

I (-7, 2) R (2, 1) T (1, -2)

U (-2, -1) E (-1, 2) P (-1, 7)

N (-7, 7) A (7, -2) D (2, 1)

WHY DOES NOBODY TALK TO CIRCLES?__ __ __ __ __ __ __ __ __ __10 12 5 1 8 6 12 9 4 6

·

·

·

·

A b

cd

__ __ __ __ __ __ __ __ __ 7 3 9 2 4 11 12 6 6


Rotations on the coordinate plane

1.

Verbal description:


2.

Verbal description:


3.

Verbal description:


4.

Verbal description:


5.

Verbal description:


6.

Verbal description:


1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8


Name _____________________________________Date _____________________________Pd______

ba

dc

d’c’

b’a’e

f

g

h

H’

G’

F’

E’

i

j k

I’

J’ K’

l m

n

N’

L’

M’ o

p q

r O’

P’ Q’

R’

s

tu

v w

S’

T’ U’

V’W’

Use what you’ve learned so far to identify each transformation. Give both a verbal description and an algebraic representation of each transformation below.


IDENTIFYING TRANSFORMATIONS

DICE ROLL Algebraic representation transformation

1 (x, y) (x + 10, y + 5)

2 (x, y) (-x, y)

3 (x, y) (x, -y)

4 (x, y) (y, -x)

5 (x, y) (x – 2, y – 1)

6 (x, y) (-x, -y)

Take turns rolling a dice with a partner or a group. Find the number you rolled and describe the transformation shown by the algebraic representation. If your partner or group agrees with your answer, record it in the table. If not, have a discussion to determine the correct answer.

Point A (-9, -3) is translated 4 left

and 2 down. Where is A’?

Point B (-5, 5) is reflected over the x-axis. Where is

B’?

Point C (7, 6) is rotated 180°

clockwise. Where is C’?

Point D (-8, -1) is reflected over the y-axis. Where is

D’?

Point E (2, -4) is rotated 90°

clockwise. Where is E’?

Use a pencil and a paper clip to spin the spinner. Answer the question you land on, and record your answers to the right of the spinner.

A’ ______B’ ______C’ ______D’ ______E’ ______




Name _____________________________________Date _____________________________Pd______

Each of the sticky notes below show the ordered pairs to different transformations of a figure. Fill in the letter of the sticky note that matches each transformation in the table.

Translation right

Translation left

Reflection over x-axis

Translation down

TRANSLATION UP

Reflection over y-axis

Rotation 90° clockwise




IDENTIFYING TRANSFORMATIONS

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1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

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-1-2-3-4-5-6-7-8

Answer each question, and be sure to show work when necessary.

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

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-1-2-3-4-5-6-7-8

AA’

Unit: TransformationsQuiz 1

Answers

1. ______________

2. ______________

3. ______________

4. ______________

5. ______________

6. ______________

7. ______________

8. ______________

9. ______________

10. _____________

11. _____________

12. _____________

13. _____________

14. _____________

15. _____________

Name _____________________________________Date ____________________________Pd______

3. Which is not a true statement about the transformation shown below?

A. Reflection over the y-axisB. Rotation 270° clockwiseC. Rotation 90 ° clockwiseD. Translation left

QUIZ: TRANSLATIONS, ROTATIONS AND REFLECTIONS

1. Which describes the transformation shown below?

2. Which describes the transformation shown below?

A. Translation left and upB. Rotation 180° clockwiseC. Reflection over the x-axisD. Translation right and down

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

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-1-2-3-4-5-6-7-8

B’

B

4. Which is not a true statement about the transformation shown below?

A. The two figures are congruent.B. The pre-image is in Quadrant I.C. The orientation of the figure

stayed the same.D. The transformation is a reflection.

A. The image is in Quadrant II.B. The two figures are congruent.C. The pre-image was translated to create the image.D. The orientation of the vertices did not change.

c

d e

C’

E’ D’

f

g h

F’

G’ H’


1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

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5. Which of the following transformations always preserve the orientation of a figure?

A. TranslationsB. RotationsC. ReflectionsD. Translations and Reflections

6. Triangle IJK has the coordinates listed:

I(5, -8) J(10, -8) K(7, -4)

Where is J’ after a reflection over the y-axis?

7. Which of the following is the algebraic representation for a translation 7 units left and 6 units up?

A. (x + 7, y – 6)B. (x – 7, y + 6)C. (x + 6, y – 7)D. (x – 6, y + 7)

8. Which transformation is shown by the coordinates below?

L(-1, 9) M(-8, 8) N(-3, 5)

L’(-9, -1) M’(-8, -8) N’(-5, -3)

A. Reflection over the x-axisB. Translation 8 units left and 8 units downC. Rotation 90° clockwiseD. Rotation 270° clockwise

Use the graph to answer questions 9- 11. 9. Reflect figure OPQR over the x-axis. Record the coordinates for P’.

10. Translate figure STUV 7 units down and 5 units left. Record the coordinates for T’.

11. In which Quadrant would figure STUV lie after a rotation 270° counterclockwise?

12. Which is the algebraic representation for a rotation 180° clockwise?

A. (y, x)B. (-y, x)C. (y, -x)D. (-x, -y)

13. Which transformation will always produce the same image as a rotation 90°counterclockwise?

A. A reflection over the y-axis.B. A rotation 270° clockwise. C. A rotation 90° clockwise.D. A reflection over the x-axis.

14. Point J (-8, -12) is reflected over the x-axis. Where is J’?

15. Point W(-6, 7) is rotated 90° clockwise. Where is W’?

o p

qr

t

uv

s



Name _____________________________________Date _____________________________Pd______

Harold and his friends went to a wizard camp where they took a class on spells and potions. The group tried several potions that would either cause you to grow or shrink based on the scale factor of the potion. Fill out the table below to show the effect

that the potions had on Harold and his friends.

Starting height Potion scale factor Process New height Grow or shrink?

60 inches1

260 x

12

30 inches shrink

64 inches 3

56 inches1

8

58 inches 2.5

60 inches 0.4

62 inches3

2

1. Describe in your own words how you calculated the new height after each potion.

2. List the scale factors that caused Harold and his friends to grow. What do you notice?

3. List the scale factors that caused Harold and his friends to shrink. What do you notice?

4. What do you think would happen if someone drank a potion with a scale factor of 1?


Scale factor and dilations

SCALE FACTOR

• Scale factor is a ratio of the corresponding sides in a figure:

neworiginal

or image

pre−image

• If the scale factor is _______________ than one, it will enlarge the figure.

• If the scale factor is _______________ than one, it will reduce the figure.

DILATIONS• A dilation is a transformation that either _______________________ or

________________ the size of an original figure.

• To dilate a figure, _______________ by the scale factor.

35 inches

15 inches

22 inches

10 inches

30 inches

24 inches

G

h

i G’

H’

I’15 cm12 cm

Y’X’x

w

y

z Z’W’

18 cm

12 cm12 cm

8 cm


5. Scale Factor = 25

Dimensions: _________________

6. Scale Factor = 3.553

Dimensions: _________________


Dimensions: _________________

8. Find the scale factor that was used to create the dilation below:

Scale Factor: _________________

9. Find the scale factor that was used to create the dilation below:

Scale Factor: _________________

For 5-7, dilate each rectangle by the given scale factor. Record the new dimensions.



Name _____________________________________Date _____________________________Pd______

In 1-9, state whether the given scale factor would “enlarge”, “reduce” or “preserve” the size of a figure.


____________________________


____________________________


____________________________


____________________________


____________________________


____________________________


____________________________


____________________________


____________________________

Use the rectangle shown to answer questions 10-13.

10. What will the new dimensions of the rectangle

be after a dilation with a scale factor of 94?

____________________________

11. What will the new dimensions of the rectangle

be after a dilation with a scale factor of 78?

____________________________

12. Stephanie dilated the rectangle and the dimensions of the image were 24 feet by 6 feet. What was the scale factor used?

____________________________

13. Ross dilated the rectangle and the dimensions of the image were 80 feet by 20 feet. What was the scale factor used?

____________________________

32 feet

8 feet


Scale factor and dilations

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1. Dilate the rectangle shown by a scale factor of 13. Record the coordinates in the table.

How can we represent the dilation algebraically?

__________________

2. Compare the ratios of corresponding sides. What do you notice?

3. Did the dilation change or preserve the orientation of the figure and the orientation of the vertices?


Name _____________________________________Date _____________________________Pd______

IF GIVEN THE SCALE FACTOR

• To dilate a figure on the coordinate plane, multiply the x and y values of

each ordered pair by the given _________ _____________ .

• Describe what should happen if the scale factor is >1:

• Describe what should happen if the scale factor is <1:

TO FIND THE SCALE FACTOR

• When a dilation has occurred on the coordinate plane, you can find the scale factor by choosing corresponding sides or vertices and setting up a ratio:

originalOR

pre−image

A b

cd

Pre-Image Image


Dilations on the coordinate plane

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4. Dilate the figure by a scale factor of 2. Then, record the algebraic representation.

Algebraic Representation: _________________________

5. Dilate the figure by a scale factor of 32. Then record the algebraic representation.

Algebraic Representation: _________________________

6. Find the scale factor that was used in the dilation:

___________

7. Find the scale factor that was used in the dilation:

___________

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-1-2-3-4-5-6-7-8

Pre-Image Image

Pre-Image Image

·· ··e f

gh

···

i

jk


8.S(9, 12) S’(6, 8)

9.T(10, -15) T’(12, -18)

10.U(-1, 0) U’(-9, 0)

Find the scale factor that was used to dilate each of the points below.


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1. Scale Factor: 1.512

A’ _________ B’ _________ C’ _________

Algebraic Representation: __________________

2. Scale Factor: 2 43

A’ _________ B’ _________ C’ _________


3. Scale Factor: 0.7512

A’ _________ B’ _________ C’ _________


4. Scale Factor: 12

A’ _________ B’ _________ C’ _________


1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

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-1-2-3-4-5-6-7-8


Name _____________________________________Date _____________________________Pd______

Dilate each of the figures in 1-4 by the given scale factor. Then, record the coordinates of the image as well as an algebraic representation of the dilation.

a

b

c

a

b

c

a

b

ca

b

c

··

· ···

·· · ·

·

·


Dilations on the coordinate plane

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

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1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

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5.

Scale Factor: __________________


6.

Scale Factor: __________________


7.

Scale Factor: __________________


8.

Scale Factor: __________________


9.G (-16, 8) G’ (-14, 7)H (-8, 0) H’ (-7, 0)

I (0, 8) I’ (0, 7)

Scale Factor: __________________


10.D (1, -2) D’ (8, -16)E (0, -3) E’ (0, -24)F (-1, 2) F’ (-8, 16)

Scale Factor: __________________


In 5-10, use the graph or the given coordinates of a dilation to determine the scale factor that was used. Then, give an algebraic representation of the dilation.

u

U’

v

V’

w

w’

x

X’


1. a. Describe the transformation shown:

b. What do you notice about corresponding side lengths and angles?

c. Write a similarity or congruency statement:

2. a. Describe the transformation shown:

b. What do you notice about corresponding side lengths and angles?

c. Write a similarity or congruency statement:


Properties of transformations


Name _____________________________________Date _____________________________Pd______

congruency

• If a transformation produces an image with the same _________and

_____________ as the pre-image, the figures are ____________________ .

• The symbol for congruency is:

• A congruency statement for the triangles

shown might be:

similarity

• If a transformation produces an image with ________________________

sides and _________________ angles, the figures are ________________.

• The symbol for similarity is:

• A similarity statement for the triangles

shown might be:

a

b

c A’

B’

C’

a

b

c A’

B’

C’

A

b

c A’

B’

C’

A

b

cA’ C’

B’

A

A’

Transformation Alg. Rep. size Orientation

Translate ABC11 units left and 1 unit up.

(x – 11, y + 1)

Congruent Same

Reflect the new image over the x-axis.

(x, -y) Congruent Changed

Rotate the newimage 90°clockwise.

(y, -x) Congruent Changed

Dilate the new image by a scale factor of 0.5.

(.5x, .5y) Similar Same

3. Use the figure below and follow the steps in the table. Include an algebraic representation of each transformation. For size, state whether the image is congruent or similar. For orientation, state whether it stayed the same or changed.

··

·The examples below show an image after a series of two transformations. Identify the two transformations that took place.

A

b

c

4.

B

B’

CC’



5. 6.

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

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-1-2-3-4-5-6-7-8

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

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-1-2-3-4-5-6-7-8

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

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-1-2-3-4-5-6-7-8

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

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-1-2-3-4-5-6-7-8

Name _____________________________________Date _____________________________Pd______

Solve each of the problems below. Be sure to ask questions if you need more help with a topic.

I can verify the properties of transformations. 8.g.1

1. Reflect the figure over the x-axis. Then, mark the statements as true or false.

______ The corresponding sides in the pre-image and image are congruent.

______ The reflection changed the orientation of the vertices.

2. Translate the figure 8 units left and 2 units up. Then, mark the statements as true or false.

______ The pre-image is located in Quadrant III.

______ The pre-image and image are congruent figures.

3. Rotate the figure 90° clockwise. Then, mark the statements as true or false.

______ The orientation of the figure did not change.

______ The corresponding angle measures in the pre-image and image are congruent.

4. Dilate the figure by a scale factor of 2.5. Then, mark the statements as true or false.



w

x y

z

s

t

v

u

o

p q

r

k

l m

n


Unit: TransformationsReview—CCSS

TRANSFORMATIONS STUDY GUIDE


I can describe the effect of transformations by using coordinates. 8.g.3

5. Point H is located at (-7, 5). Where is H’ after a 270°clockwise rotation?

6. Point R is located at (8, 13). Where is R’ after a translation 8 units left and 6 units down?

7. Point L is located at (-3,-6). Where is L’ after a reflection over the y-axis?

8. Point B is located at (4,-16). Where is B’ after a dilation

with a scale factor of 34?

9. Point W is located at (6, 2). Where is W’ after a 180°counterclockwise rotation?

10. Point Q is located at (-9, 10). Where is Q’ after a translation 4 units right and 11 units down?


Match each of the descriptions with the correct algebraic representation of the transformation.

_______11. Reflection over the x-axis

_______12. Rotation 90° counterclockwise

_______13. Translation 2 left and 2 up

_______14. Dilation; Scale Factor: 2

_______15. Rotation 180° clockwise

_______16. Translation 2 right and 2 down

_______17. Reflection over the y-axis

A. (-x, -y)

B. (2x, 2y)

C. (x, -y)

D. (x + 2, y – 2)

E. (-y, x)

F. (x – 2, y + 2)

G. (-x, y)

H. (y, -x)


18. Point J(-3, -7) was rotated to J’(7, -3). How many degrees was the rotation?

19. Point C(12, 5) was reflected to C’(-12, 5). What was the line of reflection?

20. Point M(2, 4) was dilated to M’(9, 18). What was the scale factor, and was the dilation an enlargement or reduction?

21. Point Z(-5, -6) was translated to Z’(-8, 4). Describe the direction and distance of the translation.

I can describe a sequence of transformations. 8.g.2, 8.g.4

Answer a and b for each of the transformations below:a) Identify the two transformations that occurred.

b) Write a similarity or congruency statement for the pre-image and image.

25.

a) __________________________

__________________________

b) __________________________

26.

a) __________________________

__________________________

b) __________________________

27.

a) __________________________

__________________________

b) __________________________

I can describe congruency and similarity in transformations. 8.g.2, 8.g.4

Answer a-c for each of the transformations below:a) Identify the transformation that occurred.

b) Give an algebraic representation of the transformation. c) Write a similarity or congruency statement for the pre-image and image.

22.

a) __________________________

b) __________________________

c) __________________________

23.

a) __________________________

b) __________________________

c) __________________________

24.

a) __________________________

b) __________________________

c) __________________________


x

y

z

h

J’a

b c

d

w

x y

z

d

e

f

Y’

Z’

X’

i

K’Jk

H’ I’ A’

B’ C’

D’

Z’ w’

X’Y’

D’

e’

f’

p

q

r

R’

Q’

P’



For 28-31, describe the transformation that occurred by using the coordinates.

28.A(-6, -2) A’(-6, 2)B(-3, -6) B’(-3, 6)C(-2, -2) C’(-2, 2)

29.D(15, 10) D’(6, 4)E(5, 10) E’(2, 4)

F(10, -5) F’(4, -2)

30.G(-2, 7) G’(-7, -2) H(-4, 8) H’(-8, -4)I(-3, 5) I’(-5, -3)

31.J(11, -8) J’(1, -5)K(6, -1) K’(-4, 2)L(3, -7) L’(-7, -4)


Identify whether each of the following dilations are enlargements or reductions.

32.(0.2x, 0.2y)

33.

(45x,

45y)

34.

(54x,

54y)

35.(7.5x, 7.5y)

I can verify the properties of transformations. 8.g.1

36. Complete the table by writing “same” or “changed” to describe the effect that each transformation has on the angle measures, side lengths and orientation of a figure.

Angle measures Side lengths orientation

Translations Same Same Same

Reflections Same Same Changed

Rotations Same Same Changed

dilations Same Changed Same

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

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-1-2-3-4-5-6-7-8

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

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-1-2-3-4-5-6-7-8

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

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-1-2-3-4-5-6-7-8

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8

Name _____________________________________Date _____________________________Pd______

Solve each of the problems below. Be sure to ask questions if you need more help with a topic.

I can verify the properties of transformations.

1. Reflect the figure over the x-axis. Then, mark the statements as true or false.

______ The corresponding sides in the pre-image and image are congruent.

______ The reflection changed the orientation of the vertices.

2. Translate the figure 8 units left and 2 units up. Then, mark the statements as true or false.

______ The pre-image is located in Quadrant III.


3. Rotate the figure 90° clockwise. Then, mark the statements as true or false.


______ The corresponding angle measures in the pre-image and image are congruent.

4. Dilate the figure by a scale factor of 2.5. Then, mark the statements as true or false.



w

x y

z

s

t

v

u

o

p q

r

k

l m

n


Unit: TransformationsReview

TRANSFORMATIONS STUDY GUIDE


I can describe the effect of transformations by using coordinates.

5. Point H is located at (-7, 5). Where is H’ after a 270°clockwise rotation?

6. Point R is located at (8, 13). Where is R’ after a translation 8 units left and 6 units down?

7. Point L is located at (-3,-6). Where is L’ after a reflection over the y-axis?

8. Point B is located at (4,-16). Where is B’ after a dilation

with a scale factor of 34?

9. Point W is located at (6, 2). Where is W’ after a 180°counterclockwise rotation?

10. Point Q is located at (-9, 10). Where is Q’ after a translation 4 units right and 11 units down?


Match each of the descriptions with the correct algebraic representation of the transformation.

_______11. Reflection over the x-axis

_______12. Rotation 90° counterclockwise

_______13. Translation 2 left and 2 up

_______14. Dilation; Scale Factor: 2

_______15. Rotation 180° clockwise

_______16. Translation 2 right and 2 down

_______17. Reflection over the y-axis

A. (-x, -y)

B. (2x, 2y)

C. (x, -y)

D. (x + 2, y – 2)

E. (-y, x)

F. (x – 2, y + 2)

G. (-x, y)

H. (y, -x)


18. Point J(-3, -7) was rotated to J’(7, -3). How many degrees was the rotation?

19. Point C(12, 5) was reflected to C’(-12, 5). What was the line of reflection?

20. Point M(2, 4) was dilated to M’(9, 18). What was the scale factor, and was the dilation an enlargement or reduction?

21. Point Z(-5, -6) was translated to Z’(-8, 4). Describe the direction and distance of the translation.

I can describe a sequence of transformations.

Answer a and b for each of the transformations below:a) Identify the two transformations that occurred.

b) Write a similarity or congruency statement for the pre-image and image.

25.

a) __________________________

__________________________

b) __________________________

26.

a) __________________________

__________________________

b) __________________________

27.

a) __________________________

__________________________

b) __________________________

I can describe congruency and similarity in transformations.

Answer a-c for each of the transformations below:a) Identify the transformation that occurred.

b) Give an algebraic representation of the transformation. c) Write a similarity or congruency statement for the pre-image and image.

22.

a) __________________________

b) __________________________

c) __________________________

23.

a) __________________________

b) __________________________

c) __________________________

24.

a) __________________________

b) __________________________

c) __________________________


x

y

z

h

J’a

b c

d

w

x y

z

d

e

f

Y’

Z’

X’

i

K’Jk

H’ I’ A’

B’ C’

D’

Z’ w’

X’Y’

D’

e’

f’

p

q

r

R’

Q’

P’



For 28-31, describe the transformation that occurred by using the coordinates.

28.A(-6, -2) A’(-6, 2)B(-3, -6) B’(-3, 6)C(-2, -2) C’(-2, 2)

29.D(15, 10) D’(6, 4)E(5, 10) E’(2, 4)

F(10, -5) F’(4, -2)

30.G(-2, 7) G’(-7, -2) H(-4, 8) H’(-8, -4)I(-3, 5) I’(-5, -3)

31.J(11, -8) J’(1, -5)K(6, -1) K’(-4, 2)L(3, -7) L’(-7, -4)


Identify whether each of the following dilations are enlargements or reductions.

32.(0.2x, 0.2y)

33.

(45x,

45y)

34.

(54x,

54y)

35.(7.5x, 7.5y)

I can verify the properties of transformations.

36. Complete the table by writing “same” or “changed” to describe the effect that each transformation has on the angle measures, side lengths and orientation of a figure.

Angle measures Side lengths orientation

Translations Same Same Same

Reflections Same Same Changed

Rotations Same Same Changed

dilations Same Changed Same

Name _____________________________________Date _____________________________Pd______

1. Melanie wants to create a pattern using a transformation that will change the orientation of a figure but not the orientation of the vertices. Which transformation should she use?

A. DilationB. ReflectionC. RotationD. Translation

2. Which algebraic representation shows the effect that a reflection over the x-axis will have on the coordinates of a figure?

A. (x, -y)B. (-x, y)C. (-x, -y)D. (-y, x)

3. Translate the figure 3 units right and 7 units down. Record the coordinates of the image.

4. The coordinates below represent a triangle that was dilated.

J(-3, -12) J’(-2, -8)K(-6, -15) K’(-4, -10)L(-9, -12) L’(-6, -8)

What was the scale factor that was used in the dilation?

_______________

5. Which is the correct algebraic representation of the transformation displayed on the graph?

A. (y, -x)B. (-y, x)C. (-x, y)D. (-x, -y)

6. Which is a not a true statement about the figures shown below?

A. The image is smaller than the pre-image.B. Triangle GHI is similar to Triangle G’H’I’.C. The transformation shown is a dilation.D. Segment GH is congruent to segment G’H’.

Solve the problems below. Be sure to show your thinking.

Unit: TransformationsTest

TRANSFORMATIONS UNIT TEST

A’ ___________

B’ ___________

C’ ___________


1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

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-1-2-3-4-5-6-7-8

●

●●a

b

c

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8

ed

fGD’

E’

G’

F’

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8

i

g H

G’ H’

I’

7. Ben is going to rotate a figure in Quadrant IV 90° counterclockwise. In which Quadrant should the image be?

_______________

8. Luke is going to reflect point R(6, 10) over the y-axis. What are the coordinates for R’?

_______________

9. The table below shows the coordinates of a figure that was transformed.

Which is a correct description of the transformation?

A. Rotation 180° clockwiseB. Reflection over the x-axisC. Translation 5 units left and 2 units downD. Translation 10 units left and 4 units down

10. Rotate the figure shown 180° clockwise. Record the coordinates of the image.

11. Which of the following is the correct algebraic representation for a translation 8 units right and 4 units down?

A. (x + 8, y – 4)B. (x – 4, y + 8)C. (x – 8, y + 4)D. (8x, 4y)

12. Which is a true statement about dilations?

A. A dilation will always enlarge a figure.B. A dilation will always produce congruent

figures.C. A dilation will always produce similar figures.D. A dilation will always change the orientation of

a figure.

13. Which is a true statement about the transformation shown?

A. The graph shows a translation, and the pre-image and image are congruent.

B. The graph shows a reflection, and the pre-image and image are

congruent.

C. The graph shows a translation, and the pre-image and image are

similar.

D. The graph shows a reflection, and the pre-image and image are

similar.


Pre-Image Image

A(5, 2) A’(-5, -2)

B(6, 1) B’(-4, -3)

C(4, 5) C’(-6, 1)

J’ ___________

K’ ___________

L’ ___________


1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8j

k

l

1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1

12345678

-1-2-3-4-5-6-7-8

m

o

n M’

O’

N’

14. Which of the following algebraic representations shows a dilation that is an enlargement?

A. (13x,

13y)

B. (.1x, .1y)

C. (56x,

56y)

D. (52x,

52y)

15. A triangle in Quadrant II is going to be reflected over the y-axis. Which of the following is a true statement?

A. The image will be in Quadrant III.

B. The orientation of the figure will not change.

C. The orientation of the vertices will change.

D. The image and the pre-image will not be

congruent.

16. Triangle PQR has the following coordinates:

P(-9, -12) Q(-6, -13) R(-7, -4)

Where is Q’ after a translation 9 units right and 11 units up?

_______________

17. A figure in Quadrant II was transformed, and the image is in Quadrant III. Which could not have been the transformation?

A. A rotation 90° clockwiseB. A reflection over the x-axisC. A translation downD. A rotation 270° clockwise

18. Find the scale factor that was used in the dilation shown.

_______________

19. Which transformation would create an image and a pre-image that are similar figures?

A. A dilation with a scale factor of 1.B. A translation to the right and up.C. A dilation with a scale factor of 2.D. A reflection over the x-axis.

20. Which correctly describes the two transformations that wereused to create the image on the graph?

A. Reflection over the y-axis and a rotation 90° counterclockwiseB. Translation 10 units right and a reflection over the x-axisC. Rotation 90° clockwise and a reflection over the x-axisD. Reflection over the x-axis and a translation 6 units right


tT’


yz

X’

W’

Y’

Z’

w x

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