http://www.ck12.org Chapter 7. Similarity
7.11 Dilation
Here you’ll learn what a dilation is, how to dilate a figure, and how to find the scale factor by which the figure is
dilated.
What if you enlarged or reduced a triangle without changing its shape? How could you find the scale factor by which
the triangle was stretched or shrunk? After completing this Concept, you’ll be able to use the corresponding sides
of dilated figures 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/52562CK-12 Foundation: Chapter7DilationA
Learn more about dilations by watching the video at this link.
Guidance
Atransformationis an operation that moves, flips, or changes a figure to create a new figure. Transformations that
preserve size arerigidand ones that do not arenon-rigid.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 a
scale 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.
Example A
The center of dilation isPand the scale factor is 3. FindQ′.