You can show that the scale factor of a dilation has the same value as the scale factor of the similar figures (preimage and image), with the image length in the numerator. For the figure shown on page 575,
A dilation is an enlargement if the scale factor is greater than 1. The dilation is a reduction if the scale factor is between 0 and 1.
Enlargement center A, scale factor 2
Reduction center C, scale factor
Problem 1 Finding a Scale Factor
Multiple Choice
- enlargement; scale factor 2
- enlargement; scale factor 3
- reduction; scale factor
- reduction; scale factor 3
The image is larger than the preimage, so the dilation is an enlargement. Use the ratio of the lengths of corresponding sides to find the scale factor.
Think
Why is the scale factor not
The scale factor of a dilation always has the image length (or the distance between a point on the image and the center) in the numerator.
✓ Got It?
In Got It 1, you looked at a dilation of a figure drawn in the coordinate plane. In this book, all dilations of figures in the coordinate plane have the origin as the center of dilation. So you can find the dilation image of a point P(x, y) by multiplying the coordinates of P by the scale factor n.
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs