Transcript 9-5 Dilations - Gallatin Gateway School

Dilations: (Stretching/Shrinking)
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Dilations use a scale factor to reduce or
enlarge shapes.
Every dilation has a center and a scale
factor. Most of the time it is the origin (0, 0)
Scale Factor: tells you how many times
larger or smaller your image will be.
The new shape and the image are similar.
Dilations are also called similarity
transformations.
Finding a Dilation
To find a dilation with center C and
scale factor n, you can use the
following two rules.
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The image C is itself (meaning C’=C)
For any point R, R’ is on CR and CR’ =
n•CR.
How do we locate dilation images?
A dilation is a transformation who
preimage and image are similar. A
dilation is not an isometry.
 Every dilation has a center and a
scale factor n, n >0. The scale factor
describes the size change from the
original figure to the image.
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Example 1:
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Quadrilateral ABCD
has vertices A(-2, 1), B(-2, 1), C(2,
1) and D(1, -1).
Find the
coordinates of the
image for the
dilation with a
scale factor of 2
and center of
dilation at the
origin.
C’
B’
B
A
A’
C
D
D’
Example 2:
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F(-3, -3), O(3, 3), R(0, -3) Scale factor
1/3
O
O’
F’
F
R’
R
Example 3:
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T(-1, 0), H(1, 0), I(2, -2), S(-2, -2)
Scale factor 4
T
T’
S
S’
H
H’
I
I’
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The dilation is an
enlargement if the
scale factor is > 1.
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The dilation is a
reduction if the
scale factor is
between 0 and 1.
Finding a Scale Factor
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The blue triangle is a dilation image
of the red triangle. Describe the
dilation.
The center is X. The image is larger than the
preimage, so the dilation is an enlargement.
X 'T ' 4  8
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XT
4
Finding a Scale Factor
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The blue quadrilateral is a dilation
image of the red quadrilateral.
Describe the dilation.
Graphing Dilation Images
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∆PZG has vertices P(2,0), Z(-1, ½), and G (1, 2).
What are the coordinates of the image of P for
a dilation with center (0,0) and scale factor 3?
a) (5, 3) b) (6,0) c) (2/3, 0) d) (3, -6)
Graphing Dilation Images
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Solution:
The scale factor is 3,
so use the rule:
(x, y)(3x, 3y).
P(2,0) P’(3•2, 3•0)
or P’(6, 0).
The correct answer
is B.
What are the
coordinates for G’
and Z’?