8th Grade Unit 7 Review
Some questions (c) 2015 by Progress Testing.
Some questions (c) 2015 by Region 10 Educational Service Center.
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1
Triangle ABC and triangle A'B'C' are shown below.
Why is it certain that triangle A'B'C' is a dilation of triangle ABC?
A
Because the areas of the triangles are equal to each other
B
Because triangle ABC and triangle A'B'C' are both right triangles
C
Because triangle A'B'C' is a y-axis reflection of triangle ABC
D Because the side lengths of the triangles are proportional
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Triangle ABC has vertices A(2,3),
B(4,5), and C(6,1).
If ΔABC is dilated by a scale factor of and has the origin as the center of
dilation, what are the coordinates of
B'?
F
B’(3, 4.5)
G
B’
H
B’
J
B’
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3
Carlos drew a scale picture of his backyard for his landscaper. He wants a water
feature in the center of the yard which will be in the same shape as the yard.
What is the scale factor used to arrive at the image of A'B'C'D' that is to be his water
feature?
A
B
C
D 2
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What is the scale factor of the dilation applied to ΔDEF to produce ΔD'E'F'?
F
G
H 1
J
2
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What is the scale factor of the dilation applied to rectangle JKLM to produce rectangle
J'K'L'M'?
A
B
1
C
2
D 4
6
A triangle is to be dilated with a scale
factor of 2. Which algebraic
representation represents this
dilation?
F
(x, y) → (2x, y)
G (x, y) → (2x, 2y)
H (2x, 2y) → (x, y)
J
(2x, y) → (x, y)
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7
A rectangle has vertices E(-4, 8), F(2,
8), G(2, -2) and H(-4, -2). The
rectangle is dilated so that G' is
located at (5, -5). Which algebraic
representation represents this
dilation?
A
B
C
D
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8
Quadrilateral ABCD was dilated with the origin as the center of dilation to create
quadrilateral A'B'C'D.
Which rule best represents the dilation that was applied to quadrilateral ABCD to create
quadrilateral A'B'C'D ?
F
(x, y) → (0.4x, 0.4y)
G (x, y) → (x + 3, y + 1.5)
H (x, y) → (2.5x, 2.5y)
J
(x, y) → (x - 1.5, y + 3)
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Figure S, the small arrow, was dilated with the origin as the center of dilation to create
Figure T, the large arrow.
Which rule best represents the dilation that was applied to Figure S to create Figure T?
A
B
C
D
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10
A quadrilateral ABCD has coordinates of A(-2, 4), B (4, 6), C(7, -2) and D(-3, 1).
The quadrilateral is translated 6 units to the left and 3 units down. What will be the
coordinates of A'B'C'D'?
F
(1, -8), (3, -2), (-5, 1), (-2, 9)
G (-8, 1), (-2, 3), (1, -5), (-9, -2)
H (-8, -1) (-2, 3), (1, -5), (-9, -2)
J
(8, -1), (2, -3), (-1, 5), (9, 2)
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Which of the following transformations does NOT preserve congruence?
A
(x, y) → (0.5x + 1, 0.5y − 2)
B
(x, y) → (−y − 3, x + 5)
C
(x, y) → (y + 2, −x − 1)
D (x, y) → (x − 3, y − 2)
12
Isabella graphed a shape. She then applied the transformation
(x, y) → (−x + 4, y − 1). Is the new shape congruent to the original shape? Why or
why not?
F
No, because the shape was dilated and rotated
G No, because the shape was dilated and translated
H Yes, because the shape was reflected and rotated
J
13
Yes, because the shape was reflected and translated
Which of the following transformations does NOT preserve congruence?
A
(x, y) → (x + 0.25, y − 4.5)
B
(x, y) → (2x, 2y)
C
(x, y) → (y, −x)
D (x, y) → (−y + 1, x + 1)
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Tyra is designing an obstacle course
15
Manuel has a small poster that he
in the shape of a rectangle.
wants to enlarge to a new poster.
The smaller poster with its
dimensions is shown.
If Tyra increases the length and
width of the obstacle course by a
factor of 3. What will be the resulting
effect on the perimeter of the new
playground?
F
The perimeter of the new
If Manuel doubles the dimensions of
the small poster, which describes the
playground will be times as
area of the new poster?
A
large as the original.
The area of the new poster is
double the area of the small
G The perimeter of the new
poster.
playground will be times as
B
four times the area of the small
large as the original.
poster.
H The perimeter of the new
playground will be three times as
large as the original.
J
The perimeter of the new
playground will be six times as
large as the original.
The area of the new poster is
C
The area of the new poster is
one-half of the area of the small
poster.
D The area of the new poster is
one-fourth of the area of the
small poster.
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A certain painting has an area of 216
square inches. A second painting has
dimensions twice the size of the first
painting. What is the area of the
second painting?
F
864 sq in
G 432 sq in
H 108 sq in
J
54 sq in
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17
The smaller rectangle is a dilation of the larger rectangle by a scale factor of .
Which of the following statements is true?
A
The perimeter of the smaller rectangle is the perimeter of the larger
rectangle.
B
The area of the larger rectangle is 4 times the area of the smaller rectangle.
C
The perimeter of the smaller rectangle is 2 units less than the perimeter of the
larger rectangle.
D The area of the larger rectangle is 2 times the area of the smaller rectangle.
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18
Rectangle ABCD is shown on the coordinate grid below.
If ABCD is dilated by a scale factor of to produce rectangle PQRS, what is the
perimeter of PQRS?
F
9
G 10
H 18
J
20
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