1. 12-7 Dilations

2. Transformations
The transformations we have studied thus far have all been isometries.
Reflection
Translation
Glide Reflection
Rotation

3. Dilations The last transformation that we will study is the dilation.

4. Dilations
A dilation is a transformation whose preimage and image are similar.
Remember, an isometry is a transformation in which the preimage and image are congruent.
Therefore, a dilation is not, in general, an isometry.

5. Dilations
Every dilation has a center and a scale factor n, where n must be > 0.
The scale factor describes the size change from the original figure to its image.

6. Enlargements
A dilation is an enlargement if the scale factor is greater than 1. 6
Enlargement
Center C
Scale Factor 3 2 C

7. Reductions
A dilation is a reduction if the scale factor is between 0 and 1. E D B A 8
Reduction
Center C
Scale Factor ¼
C = C’ D’ E’ A’ B’ 2

8. Example Describe the dilation (from red to blue): Type of Dilation?
Enlargement
A = A’ B’ B C C’ 6 3
Center? A
Scale Factor 3

9. Example
Find the scale factor - the dashed image is a dilation of the solid image:

10. Example
Find the scale factor - the dashed figure is a dilation image of the solid figure:

11. Example
Draw the image of each figure under a dilation centered at the origin with the given scale factor:

12. Example
Draw the image of each figure under a dilation centered at the origin with the given scale factor:

13. Example
Find the image of figure LMNO under a dilation centered at the origin with the given scale factor:
1. Scale Factor of 2
L = (-6, -6)
M = (-3, 0)
N = (6, -3)
O = (0, -3)
L’ = (-12, -12)
M’ = (-6, 0)
N’ = (12, -6)
O’ = (0, -6)

14. Example
Find the image of figure LMNO under a dilation centered at the origin with the given scale factor:
1. Scale Factor of 1/3
L = (-6, -6)
M = (-3, 0)
N = (6, -3)
O = (0, -3)
L’ = (-2, -2)
M’ = (-1, 0)
N’ = (2, -1)
O’ = (0, -1)

15. Homework: p , 28-30