Transcript Dilations LESSON 9-5 Additional Examples Circle A with 3-cm diameter and center C is a dilation of concentric circle B with 8-cm diameter.

Dilations
LESSON 9-5
Additional Examples
Circle A with 3-cm diameter and center C is a dilation of
concentric circle B with 8-cm diameter. Describe the dilation.
The circles are concentric, so the dilation has center C.
Because the diameter of the dilation image is smaller, the dilation is a
reduction.
scale factor:
diameter of dilation image
3
=
diameter of preimage
8
The dilation is a reduction with center C and scale factor
3
.
8
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GEOMETRY
Dilations
LESSON 9-5
Additional Examples
The scale factor on a museum’s floor plan is 1 : 200. The
length and width on the drawing are 8 in. and 6 in. Find the actual
dimensions in feet and inches.
1
The floor plan is a reduction of the actual dimensions by a scale factor of 200 .
Multiply each dimension on the drawing by 200 to find the actual dimensions.
Then write the dimensions in feet and inches.
8 in. X 200 = 1600 in. = 133 ft, 4 in.
6 in. X 200 = 1200 in. = 100 ft
The museum floor measures 133 ft, 4 in. by 100 ft.
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GEOMETRY
Dilations
LESSON 9-5
Additional Examples
ABC has vertices A(–2, –3), B(0, 4), and C(6, –12).
What are the coordinates of the image of ABC for a
dilation with center (0, 0) and scale factor 0.75?
The scale factor is 0.75, so use the rule (x, y)  (0.75x, 0.75y).
A' is (0.75(–2), 0.75(–3)).
B' is (0.75(0), 0.75(4)).
C' is (0.75(6), 0.75(–12)).
The vertices of the reduction image of
B' (0, 3), and C' (4.5, –9).
ABC are A' (–1.5, –2.25),
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GEOMETRY