NAME
DATE
9-6
PERIOD
Study Guide and Intervention
Draw Dilations A dilation is a similarity transformation that enlarges or reduces a
figure proportionally. Dilations are completed with respect to a center point and a scale
factor.
Example
B'
Draw the dilation image of
ABC with center O and r = 2.
B
, OB
, and OC
. Label points A, B, and C
Draw OA
so that OA = 2(OA), OB = 2(OB) and
OC = 2(OC). connect the points to draw ABC.
ABC is a dilation of ABC.
B
C
O
C'
C
O
A
A
A'
Exercises
Use a ruler to draw the image of the figure under a dilation with center S and the
scale factor r indicated.
1. r = 2
1
2. r = −
4
4
2
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3'
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3
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5'
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
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3. r = 1
5
4. r = 3
8 8
4
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5
4
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9
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2
5. r = −
6. r = 1
3
1
.
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Chapter 9
)
37
,
+
+
Glencoe Geometry
Lesson 9-6
Dilations
NAME
DATE
9-6
PERIOD
Study Guide and Intervention (continued)
Dilations
Dilations In The Coordinate Plane To find the coordinates of an image after a
dilation centered at the origin, multiply the x- and y-coordinates of each point on the
preimage by the scale factor of the dilation, r.
(x, y) → (rx, ry)
Example
ABC has vertices A(−2, −2), B(1, −1), and C(0, 2). Find the image
of ABC after a dilation centered at the origin with a scale factor of 2.
Multiply the x- and y-coordinates of each vertex by
the scale factor, 2.
(x, y)
(2x, 2y)
A(−2, −2),
A(−4, −4)
B(1, −1)
B(2, −2)
C(0, 2)
C(0, 4)
Graph ABC and its image ABC
y
$
"
$'
x
0
#
#'
"'
Exercises
Graph the image of each polygon with the given vertices after a dilation centered
at the origin with the given scale factor.
y
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y
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x
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2. A(0, 0), B(3, 3), C(6, 3), D(6, -3),
1
E(3, -3); r = −
4. A(2, 2), B(3, 4), C(5, 2); r = 2.5
3
y
#
#'
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&'
y
14
12
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10
8
6
#
4
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"
2
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Chapter 9
%
0
38
2 4 6 8 10 12 14 x
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. A(-2, -2), B(-1, 2), C(2, 1); r = 2
1. E(-2, -2), F(-2, 4), G(2, 4), H(2, -2);
r = 0.5