1. Notes 49
Dilations

2. 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.

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

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

5. 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

6. 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

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

8. 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'.

9. 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).

10. Additional Example 2 Continued

11. 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

12. 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

13. 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).

14. 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

15. 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