1. Dilations: (Stretching/Shrinking)
Dilations use a scale factor to reduce or enlarge shapes.
Every dilation has a center and a scale factor. Most of the time it is the origin (0, 0)
Scale Factor: tells you how many times larger or smaller your image will be.
The new shape and the image are similar. Dilations are also called similarity transformations.

2. Finding a Dilation
To find a dilation with center C and scale factor n, you can use the following two rules.
The image C is itself (meaning C’=C)
For any point R, R’ is on CR and CR’ = n•CR.

3. How do we locate dilation images?
A dilation is a transformation who preimage and image are similar. A dilation is not an isometry.
Every dilation has a center and a scale factor n, n >0. The scale factor describes the size change from the original figure to the image.

4. Example 1:
Quadrilateral ABCD has vertices A(-2, -1), B(-2, 1), C(2, 1) and D(1, -1).
Find the coordinates of the image for the dilation with a scale factor of 2 and center of dilation at the origin. C’ B’ B C A D A’ D’

5. Example 2: F(-3, -3), O(3, 3), R(0, -3) Scale factor 1/3 O O’ F’ R’ F

6. Example 3: T(-1, 0), H(1, 0), I(2, -2), S(-2, -2) Scale factor 4 T H

7. The dilation is an enlargement if the scale factor is > 1.
The dilation is a reduction if the scale factor is between 0 and 1.

8. Finding a Scale Factor
The blue triangle is a dilation image of the red triangle. Describe the dilation.
The center is X. The image is larger than the preimage, so the dilation is an enlargement.

9. Finding a Scale Factor
The blue quadrilateral is a dilation image of the red quadrilateral. Describe the dilation.

10. Graphing Dilation Images
∆PZG has vertices P(2,0), Z(-1, ½), and G (1, -2).
What are the coordinates of the image of P for a dilation with center (0,0) and scale factor 3?
a) (5, 3) b) (6,0) c) (2/3, 0) d) (3, -6)

11. Graphing Dilation Images
Solution:
The scale factor is 3, so use the rule:
(x, y)(3x, 3y).
P(2,0) P’(3•2, 3•0) or P’(6, 0).
The correct answer is B.
What are the coordinates for G’ and Z’?