http://www.ck12.org Chapter 7. Similarity
7.12 Dilation in the Coordinate Plane
Here you’ll learn how to draw dilated figures in the coordinate plane given starting coordinates and the scale factor.
You’ll also learn how to use dilated figures in the coordinate plane to find scale factors.
What if you were given the coordinates of a figure and were asked to dilate that figure by a scale factor of 2? How
could you find the coordinates of the dilated figure? After completing this Concept, you’ll be able to solve problems
like this one.
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/52540CK-12 Foundation: Chapter7DilationintheCoordinatePlaneA
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/10316Dilations
Guidance
Adilationmakes a figure larger or smaller, but has the same shape as the original. In other words, the dilation is
similar to the original. All dilations have acenterand ascale factor. The center is the point of reference for the
dilation (like the vanishing point in a perspective drawing) and scale factor tells us how much the figure stretches or
shrinks. A scale factor is typically labeledkand is always greater than zero. Also, if the original figure is labeled
4 ABC, for example, the dilation would be 4 A′B′C′. The ’ indicates that it is a copy. This tic mark is said “prime,”
soA′is read “A prime.” A second dilation would beA′′, read “A double-prime.”
If the dilated image is smaller than the original, then the scale factor is 0 <k< 1.
If the dilated image is larger than the original, then the scale factor isk> 1.
To dilate something in the coordinate plane, multiply each coordinate by the scale factor. This is calledmapping.
For any dilation the mapping will be(x,y)→(kx,ky). In this Concept, the center of dilation will always be the
origin, unless otherwise stated.