Dilations 1

Course 3

5-6 Dilations5-6 Dilations

Course 3

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Course 3

5-6 Dilations

Warm UpMultiply.

1. 4 2. 12

3. 24 4. –36

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5-6 Dilations

3

18

10

9

–27

30

3 4

3 4

3 4

3 4

5. 4 2.5 6. 12 2.5

Course 3

5-6 Dilations

Problem of the Day

Every day, a plant grows to three times its size. Every night, it shrinks to half its size. After three days and nights, it is 6.75 in. tall. How tall was the plant at the start? 2 in.

Course 3

5-6 Dilations

Learn to identify and create dilations of plane figures.

Course 3

5-6 Dilations

Vocabulary

dilationcenter of dilation

Course 3

5-6 Dilations

Your pupils are the black areas in the center of your eyes. When you go to the eye doctor, the doctor may dilate your pupils, which makes them larger.

Translations, reflections, and rotations are transformations that do not change the size or shape of a figure. A dilation is a transformation that changes the size, but not the shape, of a figure. A dilation can enlarge or reduce a figure.

Course 3

5-6 Dilations

Every dilation has a fixed point that is the center of dilation. To find the center of dilation, draw a line that connects each pair of corresponding vertices. The lines intersect at one point. This point is the center of dilation.

Course 3

5-6 Dilations

Tell whether each transformation is a dilation.

The transformation is a dilation.

The transformation is not a dilation. The figure is distorted.

Additional Example 1: Identifying Dilations

A. B.

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5-6 Dilations




Additional Example 1: Identifying Dilations

C. D.

Course 3

5-6 Dilations


A'

B' C'

A

B C

A.

B

A

C

A'

B' C'



Check It Out: Example 1

B.

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5-6 Dilations


C.




A'

B' C'

A

B C

D.

A'

B' C'

A

B C

Course 3

5-6 Dilations

Dilate the figure by a scale factor of 1.5 with P as the center of dilation.

Additional Example 2: Dilating a Figure

Multiply each side by 1.5.

Course 3

5-6 Dilations

Dilate the figure by a scale factor of 0.5 with G as the center of dilation.

G

F H

2 cm 2 cm

2 cm

Multiply each side by 0.5.


G

F H

2 cm 2 cm

2 cm

F’ H’1 cm

1 cm

1 cm

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5-6 DilationsInsert Lesson Title Here

Course 3

5-6 Dilations

A scale factor between 0 and 1 reduces a figure. A scale factor greater than 1 enlarges it.

Helpful Hint

Course 3

5-6 DilationsAdditional Example 3A: Using the Origin as the

Center of DilationDilate the figure below by a scale factor of 2. What are the vertices of the image?

Multiply the coordinates by 2 to find the vertices of the image.

A(4, 8) A’(4 2, 8 2) A’(8, 16) B(3, 2) B’(3 2, 2 2) B’(6, 4) C(5, 2) C’(5 2, 2 2) C’(10, 4) The vertices of the image are A’(8, 16), B’(6, 4), and C’(10, 4).

ABC A’B’C’

Course 3

5-6 DilationsAdditional Example 3B: Using the Origin as the

Center of Dilation

Dilate the figure below by a scale factor of

. What are the vertices of the image?

1 3

The vertices of the image are A’(1, 3), B’(3, 2), and C’(2, 1).

ABC A’B’C’

A(3, 9) A’(3 , 9 ) A’(1, 3)

1 3

1 3

B(9, 6) B’(9 , 6 ) B’(3, 2)

1 3

1 3

C(6, 3) C’(6 , 3 ) C’(2, 1)

1 3

1 3

Multiply the coordinates by to find the vertices of the image.

1 3

Course 3

5-6 Dilations

Check It Out: Example 3A

Dilate the figure by a scale factor of 2. What are the vertices of the image?

2

4

2 4 6 8 100

6

8

10

B

C

A

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5-6 Dilations

Check It Out: Example 3A Continued

A(2, 2) A’(2 2, 2 2) A’(4, 4) B(4, 2) B’(4 2, 2 2) B’(8, 4) C(2, 4) C’(2 2, 4 2) C’(4, 8)

ABC A’B’C’

The vertices of the image are A’(4, 4), B’(8, 4), and C’(4, 8).

Course 3

5-6 Dilations

Check It Out: Example 3A Continued

2

4

2 4 6 8 100

6

8

10

B’

C’

A’

B

C

A

Course 3

5-6 Dilations

Check It Out: Example 3B

Dilate the figure by a scale factor of 0.5. What are the vertices of the image?

2

4

2 4 6 8 100

6

8

10

B

C

A

Course 3

5-6 Dilations

Check It Out: Example 3B Continued

A(4, 5) A’(4 0.5, 5 0.5) A’(2, 2.5) B(8, 5) B’(8 0.5, 5 0.5) B’(4, 2.5) C(4, 9) C’(4 0.5, 9 0.5) C’(2, 4.5)

ABC A’B’C’

The vertices of the image are A’(2, 2.5), B’(4, 2.5), and C’(2, 4.5).

Course 3

5-6 Dilations

Check It Out: Example 3B Continued

2

4

2 4 6 8 100

6

8

10

B

C

A

B’

C’

A’

Course 3

5-6 Dilations

Lesson Quiz1. Tell whether the transformation is a dilation. A(0, 4) B(5,5) C(3,3) A’(0, 8) B’(10, 10) C’(6, 6)

2 4 6

-2

-4

-6

P

AB

CC’

B’ A’

2. Dilate the figure by a scale factor of 1.5 with P as the center of dilation.3. Dilate the figure by a scale factor of 2 with the origin as the center of dilation. What are the coordinates of the image? A(2,4) B(5,6) C(6,1)

A’(4,8) B’(10,12) C’(12,2)

yes

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Dilations 1