LESSON 6.1
Assignment
Name
me
Date
te
Big and Small
Dilating Triangles to Create Similar Triangles
1. Use quadrilateral ABCD shown on the grid to complete part (a) through part (c).
a. On the grid, draw the image of quadrilateral ABCD
dilated using a scale factor of 3 with the center of
dilation at the origin. Label the image JKLM.
y
20
K
L
18
16
14
12
J
10
8
C
B
6
b. On the grid, draw the image of quadrilateral ABCD
dilated using a scale factor of 0.5 with the center of
dilation at the origin. Label the image WXYZ.
4
M
A
X
Y
2
D
W
0
2
Z
4
6
8
10
12
14
16
18
x
20
c. Identify the coordinates of the vertices of quadrilaterals JKLM and WXYZ.
Quadrilateral JKLM: J(6, 12), K(6, 18), L(18, 18), M(18, 6)
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Quadrilateral WXYZ: W(1, 2), X(1, 3), Y(3, 3), Z(3, 1)
2. The vertices of triangle ABC are A(26, 15), B(0, 5), and C(3, 10). Without drawing the figure,
determine the coordinates of the vertices of the image of triangle ABC dilated using a scale
1 with the center of dilation at the origin. Explain your reasoning.
factor of __
3
5 , and 1, ___
10 . When a
The coordinates of the vertices of the image of triangle ABC are (22, 5), 0, __
3
3
pre-image point (x, y) is dilated using a scale factor of a with the center of dilation at the origin, its
image is the point (ax, ay).
( )
(
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LESSON 6.1
Assignment
page 2
3. The vertices of trapezoid WXYZ are W(21, 2), X(23, 21), Y(5, 21), and Z(3, 2). Without drawing the
figure, determine the coordinates of the vertices of the image of trapezoid WXYZ dilated using a scale
factor of 5 with the center of dilation at the origin. Explain your reasoning.
The coordinates of the vertices of the image of trapezoid WXYZ are (25, 10), (215, 25), (25, 25),
and (15, 10). When a pre-image point (x, y) is dilated using a scale factor of a with the center of
dilation at the origin, its image is the point (ax, ay).
4. The vertices of hexagon PQRSTV are P(25, 0), Q(25, 5), R(0, 7), S(5, 2), T(5, 22), and V(0, 25).
Without drawing the figure, determine the coordinates of the vertices of the image of hexagon
PQRSTV dilated about the origin using a scale factor of 4.2. Explain your reasoning.
The coordinates of the vertices of the image of hexagon PQRSTV are (221, 0), (221, 21), (0, 29.4),
(21, 8.4), (21, 28.4) and (0, 221). When a pre-image point (x, y) is dilated using a scale factor of a
with the center of dilation at the origin, its image is the point (ax, ay).
A(2, 2), B(2, 8), C(6, 4), A9(5, 5), B9(5, 20), C9(15, 10)
y
20
B'
18
16
14
© Carnegie Learning
5. Triangle A9B9C9 is a dilation of n ABC with the
center of dilation at the origin. List the coordinates
of the vertices of n ABC and n A9B9C9. What is the
scale factor of the dilation? Explain.
12
Each coordinate of the image is 2.5 times the
corresponding coordinate of the pre-image.
So, the scale factor is 2.5.
6
10
8
C'
B
6
A'
4
C
2
A
0
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Assignments
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4
6
8
10
12
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16
18
x
20
LESSON 6.1
Assignment
page 3
Name
me
Date
te
6. On the grid, draw the image of quadrilateral QRST using the dilation (x, y) → (0.75x, 0.75y). Label the
image Q9R9S9T9.
y
10
9
S
8
7
R
S'
6
5 R'
4
T
Q
3
Q'
T'
2
1
1
2
3
4
5
6
7
8
9
x
10
© Carnegie Learning
0
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