NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Practice 8.3(C)
SCORE ___________
Use an algebraic representation to explain the effect of a given positive rational scale factor applied to two dimensional
figures on a coordinate plane with the origin as the center of dilation.
Multi-Step Example
Square MNPQ has vertices M(1, 4), N(1, 8), P(5, 8), and Q(5, 4). The square is dilated with a scale
factor of 2, centered at the origin. Write an algebraic representation for the dilation. Determine the
coordinates of square M′N′P′Q′.
The dilation is (x, y) → (2x, 2y). Multiply each coordinate of square MNPQ by 2.
M(1, 4) → (1 • 2), (4 • 2) → (2, 8)
P (5, 8) → (5 • 2), (8 • 2) → (10, 16)
N(1, 8) → (1 • 2), (8 • 2), → (2, 16)
Q(5, 4) → (5 • 2), (4 • 2) → (10, 8)
The coordinates after the dilatation are M′(2, 8), N′(2, 16), P′(10, 16), and Q′(10, 8).
1 A triangle has vertices J(−3, 8), K(7, −1), and
L(−2, 0). The triangle is dilated so that vertex K′ has
coordinates (21, −3). Which algebraic representation
represents the dilation?
3 Triangle EFG is dilated by a scale factor of 5. Which
is an algebraic representation of the dilation?
A (3x, 3y) → (x, y)
B (x, 3y) → (3x, y)
C (3x, y) → (x, 3y)
D (x, y) → (3x, 3y)
2 Rectangle ABCD has vertices A(−1, 2), B (4, 2),
C(4, −1), and (D−1, −1). Rectangle ABCD is dilated by
3
a scale factor of . Which statement is true?
4
F Rectangle ABCD and rectangle A′B′C′D′ are
congruent.
G Rectangle ABCD and rectangle A′B′C′D′ are
similar. Rectangle ABCD is larger than rectangle
A′B′C′D′.
A (x, y) → (x, y)
B (x, y) → (5x, 5y)
1
D (x, y) → (0.5x, 0.5y)
4 Which algebraic representation represents a dilation
with a scale factor of 7?
1
H Rectangle ABCD and rectangle A′B′C′D′ are
similar. Rectangle ABCD is smaller than rectangle
A′B′C′D′.
J Rectangle ABCD and rectangle A B C D are
similar. Rectangle ABCD is the same size as
rectangle A′B′C′D′.
Course 3 • Proportionality
1
C (x, y) → (5 𝑥, 5 𝑦)
1
F (7 𝑥, 7 𝑦)→ (x, y)
G (7x, 7y) → (x, y)
H (x, y) → (7x, 7y)
1
1
J (x, y) → (7 𝑥, 7 𝑦)
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NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Practice 8.3(C) (continued)
5 A rectangle with coordinates A(0, 0), B(4, 0), C(4, 6),
and D(0, 6) is dilated, decreasing both dimensions by
30%. Then the image is dilated, increasing both
dimensions by 50%. The origin is the center of both
dilations. What is the perimeter of the final image, P″?
Record your answer and fill in the bubbles on your
answer document. Be sure to use the correct place
value.
6 Rectangles ABCD and A′B′C′D′ are shown on the
coordinate plane. Which algebraic representation
shows how the coordinates of rectangle A′B′C′D′ were
found?
SCORE ___________
8 Quadrilateral STUV with vertices S(−5, −2), T(−4, 7),
5
U(0, 5), and V(3, −6) is dilated by a scale factor of 3.
Which statement is false?
A Quadrilateral STUV is larger than quadrilateral
S′T′U′V′.
B Quadrilateral STUV and quadrilateral S′T′U′V′ are
similar.
C The algebraic representation of the dilation is
5 5
(x, y) → ( 𝑥, 𝑦)
3
3
D Quadrilateral STUV is smaller than quadrilateral
S′T′U′V′.
9 Triangles KLM and K′L′M′ are shown on the
coordinate plane. Which algebraic representation
shows how to find the coordinates of triangle K′L′M′?
1
1
A (2 𝑥, 2 𝑦)→ (x, y)
1
1
B (x, y) → (2 𝑥, 2 𝑦)
C (2x, 2y) → (x, y)
D (x, y) → (2x, 2y)
7 Which algebraic representation represents a dilation
1
with a scale factor of 3 ?
F (3x, 3y) → (x, y)
1
1
G (3 𝑥, 3 𝑦)→ (x, y)
1
3
1
3
H (x, y) → ( 𝑥, 𝑦)
J (x, y) → (3x, 3y)
3
3
2
2
F (2 𝑥, 2 𝑦)→ (x, y)
G (3 𝑥, 3 𝑦)→ (x, y)
3
3
H (x, y) → (2 𝑥, 2 𝑦)
2
3
2
3
J (x, y) → ( 𝑥, 𝑦)
10 A triangle has vertices A(0, 5), B(4, –6) , and C(5, 3).
The triangle is dilated so the vertex C′ is at (10, 6).
Which algebraic representation represents the
dilation?
A (2x, 2y) → (x, y)
B (x, 2y) → (2x, y)
C (2x, y) → (x, 2y)
D (x, y) → (2x, 2y)
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Course 3 • Proportionality
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Practice 8.3(C)
SCORE ___________
Student Answer Document
Fill in the correct answer. For gridded-response questions, write your answers in the boxes on the answer grid and
fill in the bubbles to match your answers.
1
6
2
7
3
8
4
9
5
10
Course 3 • Proportionality
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