CK-12 Geometry-Concepts

7.11. Dilation http://www.ck12.org

2. 4 ABCis a dilation of 4 DEF. IfPis the center of dilation, what is the scale factor?


3. Find the scale factor, given the corresponding sides. In the diagram, theblackfigure is the original andPis the
   center of dilation.

Answers:

1. The perimeter ofKLMN= 12 + 8 + 12 + 8 =40. The perimeter ofK′L′M′N′= 24 + 16 + 24 + 16 =80. The ratio
   is 80:40, which reduces to 2:1, which is the same as the scale factor.


2. Because 4 ABCis a dilation of 4 DEF, then 4 ABC∼4DEF. The scale factor is the ratio of the sides. Since
   4 ABCis smaller than the original, 4 DEF, the scale factor is going to be less than one,^1220 =^35.

If 4 DEFwas the dilated image, the scale factor would have been^53.

3. Since the dilation is smaller than the original, the scale factor is going to be less than one. 208 =^25

Explore More

In the two questions below, you are told the scale factor. Determine the dimensions of the dilation. In each diagram,
theblackfigure is the original andPis the center of dilation.

1.k= 4

2.k=^13