CK-12 Geometry Concepts

http://www.ck12.org Chapter 7. Similarity

Practice

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

In the question below, find the scale factor, given the corresponding sides. In the diagram, theblackfigure is the
original andPis the center of dilation.

3.

4. Find the perimeter of both triangles in #1. What is the ratio of the perimeters?
   5.WritingWhat happens ifk=1?

ConstructionWe can use a compass and straight edge to construct a dilation as well. Copy the diagram below.

6. Set your compass to beCGand use this setting to mark off a point 3 times as far fromCasGis. Label this
   pointG′. Repeat this process forCOandCDto findO′andD′.


7. ConnectG′,O′andD′to make 4 D′O′G′. Find the ratios,D

′O′

DO,

O′G′

OG and

G′D′

GD.

8. What is the scale factor of this dilation?


9. Describe how you would dilate the figure by a scale factor of 4.


10. Describe how you would dilate the figure by a scale factor of^12.


11. The scale factor between two shapes is 1.5. What is the ratio of their perimeters?


12. The scale factor between two shapes is 1.5. What is the ratio of their areas? Hint: Draw an example and
    calculate what happens.


13. Suppose you dilate a triangle with side lengths 3, 7, and 9 by a scale factor of 3. What are the side lengths of
    the image?


14. Suppose you dilate a rectangle with a width of 10 and a length of 12 by a scale factor of^12. What are the
    dimensions of the image?


15. Find the areas of the rectangles in #14. What is the ratio of their areas?