2-3 Dilations
Determine the coordinates of the vertices of
the figure after a dilation with the given scale
factor k. Then graph the original image and the
dilation.
1. C(1, 4), A(2, 2), T(5, 5); k = 2
2. R(1, 1), S(1, 7), T(5, 7), U(5, 1); k =
ANSWER: ANSWER: C′(2, 8), A′(4, 4), T′(10, 10)
2. R(1, 1), S(1, 7), T(5, 7), U(5, 1); k =
3. Refer to Exercises 1 and 2. Write an algebraic
representation for each dilation.
Exercise 1: __________________
Exercise 2: __________________
ANSWER: Exercise 1:
Exercise 2:
4. Refer to Exercises 1 and 2. Compare and contrast
each pair of figures. Are the figures congruent?
Explain.
ANSWER: ANSWER: eSolutions Manual - Powered by Cognero
Sample answer: Each pair of figures is the same
shape, but the figures are not the same size. So, Page
the 1
figures are not congruent.
ANSWER: Exercise 1:
2-3 Dilations
Exercise 2:
4. Refer to Exercises 1 and 2. Compare and contrast
each pair of figures. Are the figures congruent?
Explain.
ANSWER: Sample answer: Each pair of figures is the same
shape, but the figures are not the same size. So, the
figures are not congruent.
5. A graphic designer created a logo on
Use a problem-solving model to solve this
problem.
11. Malik uses a dilation in a perspective drawing. Using
the origin as the center of the dilation, he dilates
Rectangle I to obtain Rectangle II. Which option describes the change in perimeter, using the
following variables?
-by 11-inch
paper. In order to be placed on a business card, the
logo needs to be
inches by inches. What is the scale factor of the dilation?
ANSWER: PI = perimeter of Rectangle I
6. Darian wants to build a regulation-size pool table that
is 9 feet in length. The plans he ordered are 18 by 36
inches. What is the scale factor of the dilation he
must use to build the regulation pool table?
PII = perimeter of Rectangle II
SF = scale factor of the dilation
A. PI = SF × PII
ANSWER: B. PI = (SF)2 × PII
3
7. Organize Ideas In each part of the graphic organizer, sketch an image of pentagon MNOPQ
after a dilation within the given parameters.
C. PII = SF × PI
2
D. PII = (SF) × PI
ANSWER: C. PII = SF × PI
12. Fina is an architect. She drew quadrilateral ABCD to
represent a window. Then, using the origin as the
center, she dilated it to obtain the larger quadrilateral
A'B'C'D'. Which statement is true?
ANSWER: Use a problem-solving model to solve this
problem.
11. Malik uses a dilation in a perspective drawing. Using
the origin as the center of the dilation, he dilates
Rectangle I to obtain Rectangle II. Which option eSolutions
Manual - Powered by Cognero
describes the change in perimeter, using the
following variables?
A. m∠A' = 1.5 × m∠A
B. m∠A' = 2.25 × m∠A
C. area of A'B'C'D' = 1.5 × area of ABCD
D. area of A'B'C'D' = 2.25 × area of ABCD
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D. PII = (SF) × PI
ANSWER: = SF × PI
2-3 C. P
Dilations
II
12. Fina is an architect. She drew quadrilateral ABCD to
represent a window. Then, using the origin as the
center, she dilated it to obtain the larger quadrilateral
A'B'C'D'. Which statement is true?
A. m∠A' = 1.5 × m∠A
B. m∠A' = 2.25 × m∠A
C. area of A'B'C'D' = 1.5 × area of ABCD
D. area of A'B'C'D' = 2.25 × area of ABCD
ANSWER: D. area of A'B'C'D' = 2.25 × area of ABCD
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