Name: ______________________________ Period: __________ Date: ___________

Scale Factor =

∆ABC has been enlarged by a scale factor of 3. What are the coordinates of its image? A (1,1) A’( , ) B (1,3) B’( , ) C (3,1) C’( , )

Dilations

Dilations

Dilations

“Enlarges” or “Reduces” a figure using a scale factor.

A

B

C 2

2

A’ side length

B’

C’

6

6

1. What is the relationship between the new coordinates and the scale factor?

2. If ∆ABC is dilated by a scale factor of 4, what

are the coordinates of ∆A’B’C’? 3. If ∆ABC is dilated by a scale factor of 1/3, what

are the coordinates of ∆A’B’C’?

A dilation with a scale factor greater than 1

is called an _______________.

The image is _________________ than the

original.

A dilation with a scale factor less than 1 is

called a ___________________.

The image is ____________________ than

the original.

B

C

A’

B’

C’

A

Practice: 1. A rectangle is dilated with a scale factor of 0.6. Is the image a reduction or an enlargement? 2. 3. Find the coordinates of the image of quadrilateral KLMN after a dilation with a scale factor of 3/2.

4. You are reducing a digital photo that is 2 in. high and 3 in. wide. If the reduced photo is

in. high, what is

its width? 5. Find the coordinates of the image of quadrilateral RSTU after a dilation with the given scale factor. Graph

the image.

a. scale factor: 2 b. scale factor

a. Figure A has been dilated to figure A’. What is its scale factor?

b. Figure B has been dilated to figure B’. What is its scale factor?

R U

T S

K N

M L

A

A’

B B’

K( , ) _K’_________________ L( , ) _L’_________________ M( , ) _M’_________________ N( , ) _N’_________________

R( , ) ________________ _______________

S( , ) ________________ _______________

T( , ) ________________ _______________

U( , ) ________________ _______________

WHAT EFFECT DOES SCALE FACTOR HAVE ON PERIMETER? 6. ∆A’B’C’ is the image of ∆ABC after a dilation.

7. List the dimensions, the area, and perimeter of rectangle HIJK?

Dimensions: _____________________________

Area: _____________ Perimeter: _____________ 8. Dilate the image by 0.5.

Dimensions: _____________________________

Area: _____________ Perimeter: _____________ 9. Write the ratio of the dilated perimeter to the original perimeter. Do the same for the areas.

10. Multiply the original perimeter by the scale factor. 11. Multiply the original area by (scale factor)2.

Scale Factor

Perimeter of Original Figure

Perimeter of the Dilation

SF SF2 Area of

Original Figure Area of

the Dilation

1 10

RSTU (2 by 3)

1 1 6

RSTU (2 by 3)

2 10

R’S’T’U’ (4 by 6)

2 4 6

R’S’T’U’ (4 by 6)

3 10

R’’S’’T’’U’’ (6 by 9)

3 9 6

R’’S’’T’’U’’ (6 by 9)

4 10

R’’’S’’’T’’’U’’’ (8 by 12)

4 16 6

R’’’S’’’T’’’U’’’ (8 by 12)

What is the result when the original perimeter is multiplied by the scale factor used to dilate the figure?

What is the result if the original area is multiplied by the scale factor squared?

A

B

C 10 cm

7 cm

A’

B’

C’

24 cm 28 cm

What is the ratio of the perimeter of ∆A’B’C’ to the perimeter of ∆ABC?

R U

T S

2

3

J

K

I

H

SCALE FACTOR and ITS EFFECT ON PERIMETER and AREA.

Name: ________________________ Period: ____________ Date: ___________

Mixed Practice Homework

Translations, Reflections, Rotations, Dilations, Similar Figures, Scale Factor 1. Determine if the following polygons are similar.

a. b.

2. ∆ABC is similar to ∆EFG. Find the value of x.

Then find the scale factor if ∆ABC is dilated to form ∆EFG?

3. Quadrilateral WXYZ is similar to quadrilateral LMNP.

Find the values of x and y.

4. Graph the polygon with the given vertices. Dilate by the scale factor K and graph the image.

L(−2, −2), M(−2, −6), N(−6,−10) , Q(−6,0); k =

5. You are making a large gingerbread house that is

similar in shape to a real house. The real house is 25 feet tall and 40 feet wide. The gingerbread house is 2.5 feet tall. How wide should you make the gingerbread house?

6. Use the graph to tell what type of transformation is

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

Use the graph below for questions 7 and 8. 7. Circle N passes through points (1,1), (5,5), (9,1), and

(5,-3). If you slide the circle 2 units up and 2 units to the left, what will be the new coordinates of the center of circle N?

A (5,3) B (4,2) C (3,3) D (3,2) 8. If you slide triangle DEF 2 units down and 1 unit to

the right, what will be the new coordinates of vertex F?

A (1,1) B (1,5) C (2,1) D (2,2) 9. Margie wants to slide the triangle so that the

coordinates for vertex P are (6,1). Write a rule that tells how Margie should slide the triangle.

10. If trapezoid ABCD is reflected across the y-axis, what will be the new coordinates of the vertices? Graph the image.

AA” A 11. Cheryl drew triangle KLM as shown on the graph

below.

She began to draw a translation of triangle KLM as shown on the graph below. What should the coordinates for vertex K’ be?

A’= _________ B’ = _________ C’ = _________ D’ = _________

12. If triangle RST is reflected across the y-axis, what will be the new coordinates of its image?

13. Which of the following appears to be a reflection

over ̅̅ ̅ ?

14. Describe the transformation below. 15. EFGH is the image of ABCD after dilation. The

vertices of ABCD and EFGH are listed below A (-1,2) E(-4,8)

B (3,2) F(12,8) Graph the figures below.

C (3,-1) G(12,-4)

D(-1,-1) H (-4,-4) a. What is the scale factor? b. What is the perimeter of ABCD?

c. How is the ratio of the perimeter of EFGH to the perimeter of ABCD related to the scale factor?

d. What is the area of ABCD?

e. How is the ratio of the area of EFGH to the area of ABCD related to the scale factor?

R’= _________ S’ = _________ T’ = _________

16. The vertices of triangle JLK are listed below. J(-4,-3) K(-2,0) L(1,2)

Kim rotated the triangle 90° clockwise. Describe and correct the error Kim made when finding the coordinates of the vertices of the rotated image.

17. Graph ∆LMN with vertices L(2,0), M(2,3), and

N(6,0). Then graph its image after the following transformations.

a. Rotate 180°. b. Translate using (x, y) (x – 3, y – 4)

18. Graph ∆LMN with vertices L(2,0), M(2,3), and N(6,0). Then graph its image after the following transformations.

a. Rotate 90° counterclockwise. b. Reflect over the y-axis.

Kim’s Work

(x,y) (-y,x) J(-4,-3) J’ (3,-4) K(-2,0) K’(0,-2)

L(1,2) L’(-2,1) The vertices are: (3,-4), (0,-2), and (-2,1)