Math 8: Similarity
Section #1: Dilation on the coordinate plane 8.G.3.
Corresponds with Module 3, Lessons 3 & 6.
Notes #41A
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Key Concept!
Dilation: a transformation that changes the _____________ of a figure. Therefore it is
not a ___________________________ because rigid transformations preserve size.
Dilations create figures that are the __________ __________, but that is not enough to
prove that two figures are similar.
A dilation can either
or
the size of a figure.
Exploratory Challenge
Two geometric figures are said to be similar if they have the same shape but not necessarily
the same size. Using that informal definition, are the following pairs of figures similar to one
another? Explain.
Pair A:
Pair B:
Pair C:
Pair D:
 A dilation is performed by _________________ each point of a figure by a given
scale factor (r).
1) The vertices of ABC are A(1, 3), B(3, 2), and C(2, 0). Find the image of ABC
after a dilation from the origin with a scale factor of 2, or r = 2
 If the r > 1 (scale factor), then the dilation ______________________ the figure.
2) The vertices of ABC are A(2, 5), B(6, 2), and C(7, 4). Find the image of ABC
after a dilation from the origin with a scale factor of
1
1
, or r = .
2
2
 If the 0 < r < 1 (scale factor), then the dilation ________________ the figure.
Lesson Summary
Dilation has a __________________________ effect on the coordinates of a point in the plane.
Given a point (𝒙, 𝒚) in the plane, a dilation from the origin with scale factor 𝒓 moves the point
(x, y) to (
)
For example, if a point (𝟑, −𝟓) in the plane is dilated from the origin by a scale factor of 𝒓 = 𝟒,
then the coordinates of the dilated point are (
)
Math 8: Similarity
Section #1: Dilation on the coordinate plane 8.G.3.
Corresponds with Module 3, Lessons 3 & 6.
HW #41
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1. The triangle 𝐴𝐵𝐶, shown on the coordinate plane below, is dilated from the origin by scale factor
𝑟 = 2. What is the location of triangle 𝐴′𝐵′𝐶′? Draw and label it on the coordinate plane.
2. The triangle 𝑌𝐸𝑆, shown on the coordinate plane below, is dilated from the origin by scale factor
1
𝑟 = 2. What is the location of triangle Y′𝐸′𝑆′? Draw and label it on the coordinate plane.
3.) Perform a dilation of 2 to the object below.
Work Space
Y
U
P
R
4.) Perform a dilation of
1
2
Work Space
R
S
U
T
Math 8: Similarity
Section #1: Dilation on the coordinate plane 8.G.3.
Corresponds with Module 3, Lessons 3 & 6.
HW #41.5
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1. The rectangle 𝐴𝐵𝐶𝐷, shown on the coordinate plane below, is dilated from the origin by scale
3
factor 𝑟 = 2. A) Will the size of rectangle 𝐴𝐵𝐶𝐷 increase or decrease? What is the location of its
image? Draw and label it on the coordinate plane.
B) Find the ratio between the areas of rectangle 𝐴𝐵𝐶𝐷 and its image. What do you notice about this
ratio? (Hint: Area of a rectangle = Length × Width)
2. The triangle 𝐴𝐵𝐶, shown on the coordinate plane below, is dilated from the origin by scale factor
2
𝑟 = 3. A) Will the size of triangle 𝐴𝐵𝐶 increase or decrease? What is the location of its image? Draw
and label it on the coordinate plane.
B) Find the ratio between the areas of rectangle 𝐴𝐵𝐶𝐷 and its image. What do you notice about this
1
ratio? (Hint: Area of a triangle = 2 (𝑏𝑎𝑠𝑒 × ℎ𝑒𝑖𝑔ℎ𝑡))