1. 8.2.7 Dilations

2. TIP: All dilations are similar figures
Vocabulary
TIP: All dilations are similar figures
Dilation – A transformation in which an object is made bigger or smaller from the same point
Center of Dilation – The point from which an object dilates

3. Identifying a Dilation

4. Your Turn!

5. Scale Factor
Scale Factor – The side length ratio of two similar figures
To dilate a figure in the coordinate plane, using the origin as the center of dilation, multiply the coordinates of each original vertex by the scale factor.

6. Scale Factor
Example: if a triangle’s coordinates are (0, 2) (2, 2) (2,0) and the scale factor for its dilation is 3, then the new coordinates would be (0, 6) (6, 6) (6, 0)
Note: When the scale factor is greater than 1, the dilation is an enlargement. When the scale factor is less than 1, the dilation is a reduction. These are called TYPES of dilations: enlargement or reduction

7. Scale Factor Example
(0, 2)
(2, 2)
(2,0) x3
(0, 6)
(6, 6)
(6, 0)

8. Dilating a Figure Vertices of ABC (3x, 3y) Vertices of A’B’C’ A (1, 3)
Draw the image of Triangle ABC after a dilation with a scale factor of 3. Identify the type of dilation.
Vertices of ABC
(3x, 3y)
Vertices of A’B’C’
A (1, 3)
(3 ∙ 1, 3 ∙ 3)
A’ (3, 9)
B (2, 3)
(3 ∙ 2, 3 ∙ 3)
B’ (6, 9)
C (2, 1)
(3 ∙ 2, 3 ∙ 1)
C’ (6, 3)

9. Homework
Page 87 (#5, 6, 9, 12, 17, 18, 19, 21, 25, 33)