AnswersMO-MathematicsScale Factor

Scale Factor — Unit test Answers

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Norma Ann planned a rectangular courtyard, as shown in the scale drawing below.She decides to change the width, the shorter side of the courtyard, from 45 ft to 40 ft. Which expression finds the change in the scale factor?

Question illustration
A
StartFraction 5 inches over 45 feet EndFraction
Option A
B
StartFraction 40 feet over 5 inches EndFraction
Option B
C
StartFraction 45 feet over 40 feet EndFraction
Option C
D
StartFraction 40 feet over 45 feet EndFraction
Option D
2
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Josephine was asked to make a one-fiftieth scale model of the new water tower for her town. She constructed the model that is shown below. Not drawn to scaleWhat is the height of the town’s new water tower in feet? Round to the nearest whole number.

Question illustration
A
22 feet
B
40 feet
C
63 feet
D
113 feet
3

Theo used a map that had a ratio of to plan a road trip. He found that the distance on the map from New York City, NY, to Washington, DC, was 14.4 centimeters. How many miles would he have to drive to make that trip?

Question illustration
A
10.4
B
43.2
C
240
D
720
4

A scale factor of 5 is used to enlarge a figure as shown below.What is the area of the smaller figure, in square centimeters?

Question illustration
A
4
B
8
C
20
D
40
5

The rectangle below has been reduced by a scale factor. What is the area of the original rectangle?

Question illustration
A
25 cm²
B
75 cm²
C
375 cm²
D
450 cm²
6

Josephine was asked to make a one-fiftieth scale model of the new water tower for her town. She constructed the model that is shown below. Not drawn to scaleWhat is the height of the town’s new water tower in feet? Round to the nearest whole number.

Question illustration
A
22 feet
B
40 feet
C
63 feet
D
113 feet
7

Quinn used a scale drawing to build a soccer field near his school. Initially, he wanted the field to be 28 yards long and 17.5 yards wide. He decided to change the length of the field to 36 yards. If the width is to be changed by the same scale factor, what is the new width of the field? Express your answer to the nearest tenth.

A
18.5
B
22.5
C
25.5
D
57.6
8

A scale factor of 5 is used to enlarge a figure as shown below.What is the area of the smaller figure, in square centimeters?

Question illustration
A
4
B
8
C
20
D
40
9

Kiesha and her classmates wrote proportions for the reduction of a triangle. Which proportions are set up correctly? Select three options.

Question illustration
A
StartFraction original height over original base EndFraction = StartFraction reduction height over reduction base EndFraction
Option A
B
StartFraction original height over reduction height EndFraction = StartFraction original base over reduction base EndFraction
Option B
C
StartFraction original height over reduction base EndFraction = StartFraction reduction height over original base EndFraction
Option C
D
StartFraction reduction height over reduction base EndFraction = StartFraction original height over original base EndFraction
Option D
E
StartFraction original height over original base EndFraction = StartFraction reduction base over reduction height EndFraction
Option E
10

Kiesha and her classmates wrote proportions for the reduction of a triangle. Which proportions are set up correctly? Select three options.

Question illustration
A
StartFraction original height over original base EndFraction = StartFraction reduction height over reduction base EndFraction
Option A
B
StartFraction original height over reduction height EndFraction = StartFraction original base over reduction base EndFraction
Option B
C
StartFraction original height over reduction base EndFraction = StartFraction reduction height over original base EndFraction
Option C
D
StartFraction reduction height over reduction base EndFraction = StartFraction original height over original base EndFraction
Option D
E
StartFraction original height over original base EndFraction = StartFraction reduction base over reduction height EndFraction
Option E
11

Which of the following statements are true for using proportions to solve for missing measures? Select three options.

A
Corresponding dimensions must be in different positions in the ratios.
B
Corresponding dimensions must be in the same position in the ratios.
C
The two ratios in the proportion are equal.
D
The enlargement or reduction is proportional to the original figure.
E
The scale factor will be different for each ratio.
12

The regular pentagon below is a scale drawing of an original pentagon that was made by using a scale factor of . If each side of the pentagon has the same measure, which applies to the original pentagon? Select three options.

Question illustration
A
The scale drawing represents a reduction.
B
Each side of the original is 22 inches long.
C
One side of the model can be 1.375 inches.
D
The scale drawing is proportional to the original.
E
The scale factor is multiplied by 5.5 to get the dimensions of the original.
13

The rectangle below has been reduced by a scale factor. What is the area of the original rectangle?

Question illustration
A
25 cm²
B
75 cm²
C
375 cm²
D
450 cm²
14

The scale drawing below shows an enlargement by a scale factor of 2. What is the missing side length in the original trapezoid?

Question illustration
A
4.5
B
9
C
13.5
D
18
15

Theo used a map that had a ratio of to plan a road trip. He found that the distance on the map from New York City, NY, to Washington, DC, was 14.4 centimeters. How many miles would he have to drive to make that trip?

Question illustration
A
10.4
B
43.2
C
240
D
720
16

Abel planned for a garden to be 42 m long but found that it needs to be 24 m long to fit in his backyard. He found the change of scale below.Which is Abel’s error?

Question illustration
A
Abel should have written the ratio as .
Option A
B
Abel should have written the ratio as .
Option B
C
Abel should have divided both numbers by 6.
D
Abel should have divided both numbers by 4.
17

Below is a scale drawing of a ballroom that Mika is designing.Using the scale 1 in. : 4 m, Mika calculated the length, or the longer side of the ballroom, to be 44 m. She decides to change the scale to 1 in. : 7 m. What is the length of the new ballroom?

Question illustration
A
16 m
B
28 m
C
44 m
D
77 m
18

A scale factor of 2 is used to enlarge a figure as shown below.How many square inches is the area of the enlarged figure?

Question illustration
A
27
B
36
C
54
D
72
19

The figure on the grid is the result of enlarging a rectangle by a scale factor of 1.5.Which graph shows the original rectangle?

Question illustration
A
On a coordinate plane, a rectangle has a length of 18 and width of 4.
Option A
B
On a coordinate plane, a rectangle has a length of 8 and width of 2.
Option B
C
On a coordinate plane, a rectangle has a length of 8 and width of 3.
Option C
D
On a coordinate plane, a rectangle has a length of 12 and width of 3.
Option D
20

A rectangular magazine cover is photocopied by using a scale factor of . The length of the photocopy of the magazine cover is

Question illustration
A
enlarged by a factor of 3.
B
enlarged by a factor of .
Option B
C
reduced by a factor of 3.
D
reduced by a factor of .
Option D

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