Name: ______________________ Date: ______________________

I. Transformations

I. Use the graph below for problems 1-2.

1) Use the scale factor of 2 to dilate the pre-image.

L (-4, 2) L’

M (0, 2) M’

N (2, -4) N’

O (-4, -4) O’

Pre-image (x, y) Image ( , )

Is the image congruent to the pre-image? yes no Is the orientation of the pre-image preserved? yes no

2) Use the scale factor of ½ to dilate the pre-image.

L (-4, 2) L’

M (0, 2) M’

N (2, -4) N’

O (-4, -4) O’

Pre-image (x, y) Image ( , )

Is the image congruent to the pre-image? yes no Is the orientation of the pre-image preserved? yes no

Unit 3-2 Review Transformations, Similar Figures, and Dimensional Change

II. Look at each motion rule below and decide the transformation. Place a check mark in the box if it preserves congruence and/or orientation.

Motion Rule Transformation Preserves Congruence

Preserves Orientation

(x, y) (x+5, y-4)

(x, y) (1.5x, 1.5y)

(x, y) (-y, x)

(x, y) (x-1, y+7)

(x, y) (y, -x)

(x, y) (4.5x, 4.5y)

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

(x, y) (x-3, y-8)

(x, y) (x, -y)

(x, y) (ଵହx, ଵହy)

(x, y) (-x, y)

(x, y) (5x, 5y)

(x, y) (x+7, y-5)

(x, y) (ଵ଼x, ଵ଼y)

(x, y) (x, y)

(x, y) (x+6, y+2)

 

 

 

 

 

 

 II. Dimensional Change _____1. Rectangle ABCD is similar to rectangle A’B’C’D’.

If the perimeter of rectangle ABCD is 18 units and it is dilated by a scale factor of 2, what is the perimeter of rectangle A’B’C’D’?

A. 10 units C. 18 units B. 28 units D. 36 units

_____2. If the length of a side of a square is increased from 4 to 8, which of the following statements is true?

A. Both the area and perimeter are doubled.

B. Both the area and perimeter are quadrupled.

C. The perimeter is doubled and the area is quadrupled.

D. The perimeter is quadrupled and the area is doubled.

_____3. If the side lengths of the square below are tripled, what is NOT true about its perimeter and area?

A. The scale factor from the pre-image to the image is 3. B. The image’s perimeter will be three times larger and the area will be 9 times larger

than the pre-image. C. The image’s perimeter will be 72 mm and the area will be 324 mm. D. The image’s perimeter and area will be three times larger than the pre-image.

A B

C D

A’ B’

D’ C’

5 units

_____4. Rectangle DEFG is similar to rectangle D’E’F’G’.

If the pre-image area of rectangle DEFG is 80 units and it is dilated by a scale factor of ½, what is true about the image’s perimeter?

A. The image’s perimeter is twice as large as the pre-image’s perimeter. B. The image’s perimeter is half as large as the pre-image’s perimeter. C. The image’s perimeter is ¼ as large as the pre-image’s perimeter. D. Cannot be determined.

_____5. A 24 x 32 inch photograph is reduced so that each side is one-fourth the original size. What is the number of square inches in the smaller photograph and the new perimeter length?

      

A. 48 cm2 / 28 cm C. 6 cm2 / 8 cm

B. 28 cm2 / 48 cm D. 768 cm2 / 112 cm

_____6. The sides’ measures of two squares are shown below. The area of the smaller square is 81 square feet. What is the area of the larger square?

      

A. 9 cm2 C. 384 cm2

B. 27 cm2 D. 729 cm2

D’ E’

F’ G’

D E

F G

20 units

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1

1

M N T S90o 28o 180o 62o

'CAB ~ 'FED

C A

B

FE

D

What is the measure of �D?

62o

28o

2

R Q H L3.5 in 3.75 in 5.75 in 6.6 in

ABCD ~ A’B’C’D’

What is the length of segment C’D’?

3

A T U M9.6 ft 13.25 ft 15 ft 13 ft

Two similar trapezoids are shown below. The ratio of the lengths of the corresponding sides LO And MA is 4:5 respectively. What is the length of side AT?

M

A

T

HL

O V

E

12 ft

4

R A D LID OI ZD ZO

T R

AP O Z

I D

TRAP ~ ZOID

What side corresponds to side RA?

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2

5

T R M P10 cm 6 cm 4.5 cm 5 cm

Triangle ABC is similar to Triangle XYZ

What is the length of XY?

6

T H E F15.75 in 10.2 in 19.25 in 17 in

The dimensions of Joe’s water color painting are 8 inches by 11 inches. He placed the painting on a mat as shown below.

If the rectangles formed by the painting and the mat are similar, what is the length, x, of the mat?

14 in8 in

11 in

x

7

M T P L3 4 5 6

'HER ~ 'CAR

What is the length of AC?

8

I E T K2 m 5.33 m 6 m 12 m

A

NG

L

E

'ANG ~ 'LEG

What is the length of side x?

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3

9

U N A L360o 70o 70o 180o

What is the measure of �T?

QUAD ~ TRIM

U

Q

A

D

M T

RI

70o

70o

110o

110o

10

H T D L4.5 cm 6 cm 6.5 cm 10 cm

JKLM ~ J’K’L’M’

What is the length of segment J’M’?

11

S G N T5.25 cm 6 cm 8 cm 9.3 cm

4 cm

4 c

m

3 cm 1 cm

7 cm

w

The two figures below are similar

What is the length of side w?