1. 5-6
Dilations
Course 3
Warm Up
Problem of the Day
Lesson Presentation

2. 5-6 Dilations Warm Up Multiply. 1. 4  2. 12  3. 24  4. –36  3 9 18
Course 3
5-6
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. 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. Learn to identify and create dilations of plane figures.

5. Vocabulary
dilation
center of dilation

6. Your pupils are the black areas in the center of your eyes
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.

7. Every dilation has a fixed point that is the center of dilation
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.

8. Additional Example 1: 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.

9. Additional Example 1: 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.

10. Tell whether each transformation is a dilation.
Check It Out: Example 1
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.

11. Tell whether each transformation is a dilation.
Check It Out: Example 1
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.

12. 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.

13. Check It Out: 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.

14. Insert Lesson Title Here
Course 3
5-6
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

15. Additional Example 3A: Using the Origin as the Center of Dilation
Dilate 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’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).

16. Additional Example 3B: Using the Origin as the Center of Dilation
1 3
Dilate the figure below by a scale factor of . What are the vertices of the image?
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).

17. Check It Out: 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

18. Check It Out: 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).

19. Check It Out: Example 3A Continued10 B’ C’ A’ 8 6 C 4 2 A B 2 4 6 8 10

20. Check It Out: 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

21. Check It Out: 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).

22. Check It Out: Example 3B Continued10 C 8 6 B’ C’ A’ A B 4 2 2 4 6 8 10

23. 1. Tell whether the transformation is a dilation.
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)