1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up
Solve. 1. 2.
x = 12
x = 2.5 2

3. Problem of the Day
Missy ate one-fourth of a fruit salad and Kim ate one-eighth of the fruit salad. What fraction of the fruit salad remains? 3

4. Sunshine State Standards
MA.7.G.4.2 Predict the results of transformations and draw transformed figures, with and without the coordinate plane.

5. A dilation is a transformation that changes the size, but not the shape, of a figure. After a dilation, the image of a figure is similar to the preimage.

6. Additional Example 1A: Identifying Dilations
Tell whether each transformation is a dilation.
The figures are not similar, so the transformation
is not a dilation.

7. Additional Example 1B: Identifying Dilations
Tell whether each transformation is a dilation.
The figures are similar, so the transformation
Is a dilation.

8. Tell whether each transformation is a dilation.
Check It Out: Example 1A
Tell whether each transformation is a dilation. A B A’ B’
3 cm
6 cm C’ D’
5 cm D C
10 cm
The figures are similar, so the transformation is a dilation.

9. Tell whether each transformation is a dilation.
Check It Out: Example 1B
Tell whether each transformation is a dilation. Y X’
13 yd
6 yd
6 yd
5 yd X z z’
6 yd Y’
12 yd
The figures are not similar, so the transformation is not a dilation. 9

10. Similar figures have the same shape but not necessarily the same size.
Remember!

11. Additional Example 2: Using Dilation to Enlarge a Figure
Draw the vertices of the image of ∆ABC after a dilation by a scale factor of 2. What are the vertices of the image?
Write the coordinates of the vertices of ABC. Then multiply the coordinates by 2 to find the coordinates of the vertices of A'B'C'.

12. Additional Example 2 Continued
A’B’C’
ABC
A(0, 0) A’(0  2, 0  2) A’(0, 0)
B(1, 2) B’(1  2, 2  2) B’(2, 4)
C(3, 1) C’(3  2, 1  2) C’(6, 2)
The vertices of the image are A’(0, 0), B’(2, 4), and C’(6, 2).

13. Additional Example 2 Continued

14. Check It Out: Example 2A
Find the vertices of the image of each figure after a dilation by the given scale factor. Then draw the image.
Scale factor 3
R' (0, 12), S' (12, 6), T' (6, 3)

15. Check It Out: Example 2B
Find the vertices of the image of each figure after a dilation by the given scale factor. Then draw the image.
Scale factor 2
A' (4, 10), B' (10, 10),C' (10, 4), D' (4, 4)

16. Additional Example 3: Using a Dilation to Reduce a Figure
Draw the image of ∆DEF after a dilation by a scale factor of Then draw the image.
1 3
Write the coordinates of the vertices of DEF. The multiply the coordinates by 1/3 to find the coordinates of the vertices of D‘E‘F'.
D’E’F’
DEF
D(3, 3) D’(3  , 3  ) D’(1, 1)
1 3
E(6, 6) E’(6  , 6  ) E’(2, 2)
1 3
F(9, 3) F’(9  , 3  ) F’(3, 1)
1 3
The vertices of the image are D’(1, 1), E’(2, 2), and F’(3, 1).

17. Check It Out: Example 3A
Find the vertices of the image of each figure after a dilation by the given scale factor. Then draw the image.
1 3
Scale factor
A' (1, 2), B' (1, 4),C' (3, 4),D' (3, 2)

18. Check It Out: Example 3B
Find the vertices of the image of each figure after a dilation by the given scale factor. Then draw the image.
1 4
Scale factor
D' (1, 2), E' (2, 3), F' (3, 2)

19. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 19

20. Tell whether the transformation is a dilation. 1.
Lesson Quiz
Tell whether the transformation is a dilation. 1.
yes
2. Find the vertices of the image of ∆ABC after a dilation of a scale factor of 2. Then draw the image.
A'(2, 4), B'(4, 6), C'(8, 0) 20

21. Lesson Quiz for Student Response Systems
1. Tell whether the transformation is a dilation.
A. dilation
B. not a dilation 21

22. Lesson Quiz for Student Response Systems
2. Tell whether the transformation is a dilation.
A. dilation
B. not a dilation 22