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Prebell
WB p. 49 # 6
Types of Dilations
Similar Transformations
• Dilation – a transformation
in which a figure is made
larger or smaller with
respect to a point called
the center of dilation
• Dilations move points
a specific distance,
determined by the
scale factor, 𝑟, from
the center, 𝑂.
• Dilations always
create similar figures.
The graph below represents a dilation from center (0, 0)
by scale factor 𝑟 = 2.
• If the scale factor is between zero and one
(0 < 𝑟 < 1), the dilation is a reduction (shrinks).
– All points are pulled toward the center proportionally.
• If the scale factor is greater than one (𝑟 > 1), the
dilation is an enlargement (magnifies).
– All points are pushed away from the center
proportionally.
• What happens if the scale factor is exactly 1
(𝑟 = 1)?
The graph below represents a dilation from center (0, 0)
by scale factor 𝑟 = 4.
What effect does the dilation have on
the coordinates of dilated points?
Dilating From the Origin
• Multiply each coordinate by the scale factor.
• Point 𝐴(−2, 3) is dilated from the origin by
scale factor 𝑟 = 3. What are the coordinates
of point 𝐴′?
• Point 𝐵(−2, −5) is dilated from the origin by
3
scale factor 𝑟 = . What are the coordinates
2
of point 𝐵′?
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Triangle 𝐴𝐵𝐶 has coordinates
𝐴 2, 3 , 𝐵 −3, 4 , 𝐶 5, 7 . The triangle is being
dilated from the origin with scale factor 𝑟 = 4.
What are the coordinates of triangle 𝐴′𝐵′𝐶′?
Identify the type of dilation.
Figure 𝐷𝐸𝐹𝐺 is shown on the coordinate plane below.
The figure is dilated from the origin by scale factor
2
𝑟 = . Identify the coordinates of the dilated figure
3
𝐷′ 𝐸′𝐹′𝐺 ′ on the coordinate plane.
A rectangle has vertices 𝑊(−4, −6), 𝑋(−4, 8),
𝑌(4, 8), 𝑍(4, −6). Find its vertices after a
dilation with a scale factor of ½. Then, draw and
label the figure and its dilated image.
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