1. 7-5
Dilations
Course 3
Warm Up
Problem of the Day
Lesson Presentation

2. 7-5 Dilations Warm Up Multiply. 1. 4  2. 12  3. 24  4. –36  3 9 18
Course 3
7-5
Dilations
Warm Up
Multiply.
1. 4  
3. 24  –36 
3 4
3 4 3 9
3 4
3 4 18
–27
5. 4   2.5 10 30

3. 7-5 Dilations Problem of the Day
Course 3
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.

4. 7-5 Dilations Learn to identify and create dilations of plane figures.
Course 3
7-5
Dilations
Learn to identify and create dilations of plane figures.

5. Insert Lesson Title Here
Course 3
7-5
Dilations
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Vocabulary
dilation
scale factor
center of dilation

6. Course 3
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.

7. Course 3
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.

8. Course 3
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.

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Course 3
7-5
Dilations
Insert Lesson Title Here
A scale factor between 0 and 1 reduces a figure. A scale factor greater than 1 enlarges it.
Helpful Hint

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Course 3
7-5
Dilations
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Additional Example 1A & 1B: Identifying Dilations
Tell whether each transformation is a dilation. A. B.
The transformation
is not a dilation.
The figure is distorted.
The transformation
is a dilation.

11. Insert Lesson Title Here
Course 3
7-5
Dilations
Insert Lesson Title Here
Additional Example 1C & 1D: Identifying Dilations
Tell whether each transformation is a dilation. D. C.
The transformation
is not a dilation.
The figure is distorted.
The transformation
is a dilation.

12. 7-5 Dilations Try This: Example 1A & 1B
Course 3
7-5
Dilations
Try This: Example 1A & 1B
Tell whether each transformation is a dilation. B A C A' B' C' A. A B C B. A' B' C'
The transformation
is a dilation.
The transformation
is not a dilation.
The figure is distorted.

13. 7-5 Dilations Try This: Example 1C & 1D
Course 3
7-5
Dilations
Try This: Example 1C & 1D
Tell whether each transformation is a dilation. D. A' B' C' A B C C. A' B' C' A B C
The transformation
is not a dilation.
The figure is distorted.
The transformation
is a dilation.

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Course 3
7-5
Dilations
Insert Lesson Title Here
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.

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Course 3
7-5
Dilations
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Additional Example 2: Dilating a Figure
Dilate the figure by a scale factor of 1.5 with P as the center of dilation.
Multiply each side by 1.5.

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Course 3
7-5
Dilations
Insert Lesson Title Here
Try This: Example 2
Dilate the figure by a scale factor of 0.5 with G as the center of dilation. G F H
2 cm F’ H’
1 cm G
2 cm
2 cm F H
2 cm
Multiply each side by 0.5.

17. Additional Example 3A: Using the Origin as the Center of Dilation
Course 3
7-5
Dilations
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Additional Example 3A: Using the Origin as the Center of Dilation
Dilate 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’B’C’
ABC
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).

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Course 3
7-5
Dilations
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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
Multiply the coordinates by to find the vertices of the image.
1 3
A’B’C’
ABC
A(3, 9) A’(3  , 9  ) A’(1, 3)
1 3
B(9, 6) B’(9  , 6  ) B’(3, 2)
1 3
C(6, 3) C’(6  , 3  ) C’(2, 1)
1 3
The vertices of the image are A’(1, 3), B’(3, 2), and C’(2, 1).

19. Insert Lesson Title Here
Course 3
7-5
Dilations
Insert Lesson Title Here
Try This: Example 3A
Dilate the figure by a scale factor of 2. What are the vertices of the image? 10 8 6 C 4 2 A B 2 4 6 8 10

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Course 3
7-5
Dilations
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Try This: Example 3A Continued
A’B’C’
ABC
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)
The vertices of the image are A’(4, 4), B’(8, 4), and C’(4, 8).

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Course 3
7-5
Dilations
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Try This: Example 3A Continued 10 B’ C’ A’ 8 6 C 4 2 A B 2 4 6 8 10

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Course 3
7-5
Dilations
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Try This: Example 3B
Dilate the figure by a scale factor of What are the vertices of the image? 10 C 8 6 A B 4 2 2 4 6 8 10

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Course 3
7-5
Dilations
Insert Lesson Title Here
Try This: Example 3B Continued
A’B’C’
ABC
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)
The vertices of the image are A’(2, 2.5), B’(4, 2.5), and C’(2, 4.5).

24. Insert Lesson Title Here
Course 3
7-5
Dilations
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Try This: Example 3B Continued 10 C 8 6 B’ C’ A’ A B 4 2 2 4 6 8 10

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Course 3
7-5
Dilations
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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)
yes 2 4 6
2. Dilate the figure by a scale factor of 1.5 with P as the center of dilation. P A B C C’ B’ A’ -2
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) -4 -6
A’(4,8) B’(10,12) C’(12,2)