Pre-Algebra

7-5 Dilations7-5 Dilations

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Pre-Algebra

7-5 Dilations

Warm UpMultiply.

1. 4 2. 12

3. 24 4. –36

Pre-Algebra

7-5 Dilations

3

18

10

9

–27

30

3 4

3 4

3 4

3 4

5. 4 2.5 6. 12 2.5

Pre-Algebra

7-5 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.

Pre-Algebra

7-5 Dilations

Learn to identify and create dilations of plane figures.

Pre-Algebra

7-5 Dilations

Vocabulary

dilationscale factorcenter of dilation

Pre-Algebra

7-5 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.

Pre-Algebra

7-5 Dilations

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.

Pre-Algebra

7-5 Dilations

A scale factor describes how much a figure is enlarged or reduced. A scale factor can be expressed as a decimal, fraction, or percent. A 10% increase is a scale factor of 1.1, and a 10% decrease is a scale factor of 0.9.

Pre-Algebra

7-5 Dilations

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

Helpful Hint

Pre-Algebra

7-5 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 1A & 1B: Identifying Dilations

A. B.

Pre-Algebra

7-5 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 1C & 1D: Identifying Dilations

C. D.

Pre-Algebra

7-5 Dilations

Tell whether each transformation is a dilation.

A'

B' C'

A

B C

A.

B

A

C

A'

B' C'

The transformation is a dilation.

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

Try This: Example 1A & 1B

B.

Pre-Algebra

7-5 Dilations

Tell whether each transformation is a dilation.

C.

The transformation is a dilation.

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

Try This: Example 1C & 1D

A'

B' C'

A

B C

D.

A'

B' C'

A

B C

Pre-Algebra

7-5 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.

Pre-Algebra

7-5 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.

Pre-Algebra

7-5 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.

Try This: Example 2

G

F H

2 cm 2 cm

2 cm

F’ H’1 cm

1 cm

1 cm

Pre-Algebra

7-5 DilationsAdditional Example 3A: Using the Origin as the Center of

DilationDilate the figure in Example 3A on page 363 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’

Pre-Algebra

7-5 Dilations

Additional Example 3B: Using the Origin as the Center of Dilation

Dilate the figure in Example 3B 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

Pre-Algebra

7-5 Dilations

Try This: 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

Pre-Algebra

7-5 Dilations

Try This: 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).

Pre-Algebra

7-5 Dilations

Try This: Example 3A Continued

2

4

2 4 6 8 100

6

8

10

B’

C’

A’

B

C

A

Pre-Algebra

7-5 Dilations

Try This: 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

Pre-Algebra

7-5 Dilations

Try This: 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).

Pre-Algebra

7-5 Dilations

Try This: Example 3B Continued

2

4

2 4 6 8 100

6

8

10

B

C

A

B’

C’

A’

Pre-Algebra

7-5 Dilations

Lesson Quiz

1. 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

C

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)