Page 95 - Math Course 2 (Book 2)

Transformations: Dilations
Mo. 9

Lesson 6 Key Concept

Dilation
KEY CONCEPTS:

1. Determine whether a dilation is an If | r | > 1, the dilation is an enlargement.
enlargement, a reduction, or a If 0 < | r | < 1, the dilation is a reduction.
congruence transformation. If | r | = 1, the dilation is a congruence transformation
2. Determine the scale factor for a given
dilation.
THEOREM 9.2

MO. 9 - L6a
If a dilation with center C and a scale factor of r
transforms A to E and B to D, then ED = | r |(AB).
Determining a Dilation B

D

Vocabulary A-Z

Let us learn some vocabulary A E C

dilation Dilations
A dilation is another type of transformation that → →
may change the size of a figure which can result If r > O, P' lies on CP, and CP' = r • CP.
in a larger figure and a smaller figure than the If r < O, P' lies on CP the ray opposite CP, and CP'
→
original.
= | r | • CP.
A dilation requires a center point and a scale factor.
The letter r usually represents the scale factor. The center of a dilation is always its own image.
r = 2

A'
B' THEOREM 9.3

center A B If P(x, y) is the preimage of a dilation centered at the
origin with a scale factor r, then the image is P' (rx, ry)

C D D'

similarity transformation
are transformations that produce similar 2
figures such as dilations.
Dilation preserve angle measure,
betweenness of points, and 4 4
collinearity, but do not 1
preserve distance.
image
2 2 2
object
1

Dilation Centre
87