NAME _____________________________________________ DATE ____________________________ PERIOD _____________
9-6 Study Guide and Intervention
Dilations
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: Draw the dilation image of △ABC with center O and r = 2.
Draw ⃗⃗⃗⃗⃗
𝑂𝐴, ⃗⃗⃗⃗⃗
𝑂𝐵, and ⃗⃗⃗⃗⃗
𝑂𝐶 . Label points A′, B′, and C′ so that OA′ = 2(OA),
OB′ = 2(OB) and OC′ = 2(OC). connect the points to draw △A′B′C′.
△A′B′C′ is a dilation of △ABC.
Exercises
Use a ruler to draw the image of the figure under a dilation with center S and the scale factor r indicated.
1
1. r = 2
2. r = 2
3. r = 1
4. r = 3
2
5. r = 3
Chapter 9
6. r = 1
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Glencoe Geometry
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
9-6 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(2, 0). 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(2, 0)
C′(4, 0)
Graph △ABC and its image △A′B′C′
Exercises
Graph the image of each polygon with the given vertices after a dilation centered at the origin
with the given scale factor.
1. E(–2, –2), F(–2, 4), G(2, 4), H(2, –2);
r = 0.5
3. A(–2, –2), B(–1, 2), C(2, 1); r = 2
2. A(0, 0), B(3, 3), C(6, 3), D(6, –3),
1
E(3, –3); r = 3
4. A(2, 2), B(3, 4), C(5, 2); r = 2.5
Chapter 9
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Glencoe Geometry