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Name___________________________

Transformation Packet

DUE:

TEST:

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Transformation Vocabulary .

Transformation Related Terms Sketch Reflection

(flip across a line)

Line of reflection

Pre-image and image

Rigid

Rotation

(turn about a point in

a specific direction)

Point of rotation

Degrees

Clockwise or counterclockwise

Rigid Translation

(shifted copy)

Vertical and horizontal shift

Rigid

Dilation

(reduction or

enlargement)

Scale factor

Not rigid

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Coordinate Transformation Rules

Draw the image of rectangle ABCD under each transformation. Describe the transformation in words! List the

points of the image of rectangle ABCD (the image is called rectangle A’B’C’D ’).

1. (𝑥, 𝑦) → (−𝑥, 𝑦)

2. (𝑥, 𝑦) → (𝑥, −𝑦)

3. (𝑥, 𝑦) → (𝑥 − 3, 𝑦)

4. (𝑥, 𝑦) → (𝑥, 𝑦 + 4)

5. (𝑥, 𝑦) → (𝑥 − 2, 𝑦 − 1)

6. (𝑥, 𝑦) → (𝑦, 𝑥)

A

B

C

D

A

B

C

D

A

B

C

D

A

B

C

D

A

B

C

D

A

B

C

D

x y

A’

B’

C’

D’

Description:

x y

A’

B’

C’

D’

Description:

x y

A’

B’

C’

D’

Description:

x y

A’

B’

C’

D’

Description:

x y

A’

B’

C’

D’

Description:

x y

A’

B’

C’

D’

Description:

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7. (𝑥, 𝑦) → (−𝑦, 𝑥)

8. (𝑥, 𝑦) → (𝑦, −𝑥)

9. (𝑥, 𝑦) → (0.5𝑥, 0.5𝑦)

10. (𝑥, 𝑦) → (−0.5𝑥, −0.5𝑦)

Does the order in which a point is transformed matter?? Let’s see…..

11. (𝑥, 𝑦) → (𝑥 − 2, 𝑦 + 3) → (𝑥, −𝑦)

12. (𝑥, 𝑦) → (𝑥, −𝑦) → (𝑥 − 2, 𝑦 + 3)

What can you infer from examples 11 and 12?

A

B

C

D

A

B

C

D

A

B

C

D

A

B

C

D

A

B

C

D

A

B

C

D

x y

A’

B’

C’

D’

Description:

x y

A’

B’

C’

D’

Description:

x y

A’

B’

C’

D’

Description:

x y

A’

B’

C’

D’

Description:

x y

A’

B’

C’

D’

Description:

x y

A’

B’

C’

D’

Description:

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Summary of Coordinate Transformations

Example: Describe the transformation using

coordinate notation.

Example: Find the coordinates of the vertices

of triangle ABC after the transformation

(x,y) (x,-y).

A(–3,4) A’ ( ___,___ )

B(2 , 1)B’ ( ___,___ )

C(–1,–5) C’ ( ___,___ )

Example: Draw ABC with vertices A (4, 0),

B (0, 4), and C (0, 0). Then find the

coordinates of the vertices of the image after

the translation (x, y) → (x–4, y–3), and draw

the image.

Example: Find the coordinates of line

segment AB after the transformation

(x,y) (2x,2y).

A(5,2) A’ ( ___,___ )

B(–8 , –4)B’ ( ___,___ )

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Rectangle ABCD has coordinates A(1,6),

B(–5,–2), C(–1,–5), and D(5,3).

Graph rectangle ABCD.

Find the length of the four sides of

rectangle ABCD (use the distance

formula).

AB=

BC=

CD=

DA=

Find the area of rectangle ABCD.

Rectangle A’B’C’D’ is the result of

transforming rectangle ABCD based

on the rule (x,y)(2x,2y). What is

the name of this transformation?

Determine the coordinates for

A’B’C’D (use the rule above):

A’= B’=

C’= D’=

Graph A’B’C’D’ on the coordinate

plane at right. Compare the graphs of

ABCD and A’B’C’D’.

Find the length of the four sides of

rectangle A’B’C’D’ (use the distance

formula).

A’B’=

B’C’=

C’D’=

D’A’=

Find the area of rectangle A’B’C’D’.

Compare the side lengths and areas of ABCD and A’B’C’D’. Be specific.

What do you notice about the location of A’B’C’D’ as compared to ABCD?

Hopefully this example will help explain why the LOCATION of a figure changes

under a dilation.

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In the example on the previous page, you determined the coordinates of A’B’C’D’

after the transformation (x,y)(2x,2y). This transformation is called a

________________________. Recopy the coordinates of A’B’C’D’ below.

A’ B’ C’ D’

Determine the distance of each point above from the origin O(0,0).

OA’ OB’ OC’ OD’

Consider the original coordinates of rectangle ABCD given below.

A(1,6) B(–5,–2) C(–1,–5) D(5,3)

Determine the distance of each point above from the origin O(0,0).

OA OB OC OD

Compare OA and OA’… OB and OB’… OC and OC’…. And OD and OD’.

So a dilation not only changes the length of sides of a figure, but changes the

location of each point making up the figure by….

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Practice

1. Find the coordinates of the vertices of the image after the specified

transformation, and draw the image.

(x, y) → (x–4, y+2)

(x, y) → (y, −𝑥)

(x, y) → (0.5x, 0.5𝑦)

2. Transformations can be used to show motion. Use coordinate notation to

describe the transformation of the drummer from one picture to the next

picture.

3. Draw one triangle with vertices (2, 1), (3, 4), and

(4, 1) and a second triangle with vertices (4, 1), (3,

4), and (2, 1).Describe two different

transformations that could move the first triangle

onto the second.

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4. The vertices of quadrilateral ABCD are A(3, 4), B(2, 4), C(3, 2), and D(4, 1).

After a translation, the coordinates of A’ are (5, 1). Describe the translation

using coordinate notation. Then find the coordinates of B’, C’, and D’.

5. Determine whether or not the following statements are TRUE or FALSE.

a. _____The transformation (x,y) (x+2, y+2) applied to the ordered pairs

that form a square will result in a square that covers twice the area of the

original square.

b. _____The transformation (x,y)(x,y-2) will translate a figure left 2

units.

c. _____When reflected over the x-axis, the point (3,–5) becomes (3,5).

d. _____When reflected over the y-axis, the point (3, –5) becomes (3,5).

e. _____ If square ABCD has A(–4,1) and is rotated 90° clockwise about

the origin, then the new coordinates of A must be (1,4).

f. _____Translating a figure results in a figure similar, but not congruent to

the original figure.

g. _____ Rotating a figure results in a figure congruent to the original

figure.

h. _____The only transformation that results in a figure similar, but not

congruent to the original figure is a dilation.

6. MULTIPLE CHOICE

Rectangle A′B′C′D′ is the image of rectangle

ABCD after which of the following rotations?

A. A 90° clockwise rotation about the origin

B. A 90° counterclockwise rotation about the origin

C. A 180° rotation about the origin

D. A reflection over the y-axis.

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7. The vertices of triangle ABC are

A(–3,–1), B(–4,3), and C(1,2).

Reflect the triangle over the line

𝑦 = 𝑥. Graph the triangle and its

image.

8. The vertices of quadrilateral ABCD

are A(5,–2), B(7,–4), C(4,–7), and

D(2,–5). Rotate the figure 90°

counterclockwise. Graph the figure and

its image.

8. In the diagram, the quadrilateral is

rotated about P. What is the value

of y?

9. Graph ∆DEF with vertices D(0,3),

E(4,3), and F(0,6). Then graph its

image after translating according to the

rule (x,y) (x, y+2), then rotating 180°.

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NC FINAL Practice 1. Which rotation will carry a square onto itself?

a. 30° clockwise rotation

b. 45°counterclockwise rotation

c. 60° clockwise rotation

d. 90° counterclockwise rotation

2. Which rotation will carry a regular hexagon onto

itself?

a. 30° clockwise rotation

b. 90°counterclockwise rotation

c. 120° clockwise rotation

d. 330° counterclockwise rotation

3. Which rotation will carry a regular octagon onto

itself?

a. 30° counterclockwise rotation

b. 120°counterclockwise rotation

c. 135° clockwise rotation

d. 300° clockwise rotation

4. Which rotation will carry a regular decagon onto

itself?

a. 45° clockwise rotation

b. 72°counterclockwise rotation

c. 90° clockwise rotation

d. 148° counterclockwise rotation

5. If triangle ABC is translated 5 units down and 3

units left, which transformation would move it back

to its original location?

a. (𝑥, 𝑦) → (𝑥 + 3, 𝑦 + 5)

b. (𝑥, 𝑦) → (𝑥 − 3, 𝑦 − 5)

c. (𝑥, 𝑦) → (𝑥 + 5, 𝑦 + 3)

d. (𝑥, 𝑦) → (𝑥 − 5, 𝑦 − 3)

6. If triangle ABC is rotate 90° clockwise, which

transformation would move it back to its original

location?

a. (𝑥, 𝑦) → (−𝑥, −𝑦)

b. (𝑥, 𝑦) → (𝑦, −𝑥)

c. (𝑥, 𝑦) → (−𝑦, 𝑥)

d. (𝑥, 𝑦) → (−𝑦, −𝑥)

7. 𝑀𝑁̅̅ ̅̅ ̅ has 𝑀(1,9) and 𝑁(5,12). If 𝑀𝑁̅̅ ̅̅ ̅ is dilated with respect to the origin by a scale factor of k to produce

𝑀′𝑁′̅̅ ̅̅ ̅̅ ̅, which statement must be true?

a. 𝑀′𝑁′̅̅ ̅̅ ̅̅ ̅ has a length of 5.

b. The midpoint of 𝑀′𝑁′̅̅ ̅̅ ̅̅ ̅ is (3,10.5).

c. The line that passes through 𝑀′ and 𝑁′ has a slope of (3

4) 𝑘.

d. The line that passes through 𝑀′ and 𝑁′ intersects the y-axis at (0,8.25𝑘).

8. Triangle EGF is graphed below. Triangle EGF will be rotated 90° clockwise around the origin and will then

be reflected across the y-axis, producing an image triangle. Which additional transformation will map the image

triangle back onto the original triangle?

A rotation 270° counterclockwise around the origin

B rotation 180° counterclockwise around the origin

C reflection across the line y = − x

D reflection across the line y = x

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