AnswersTX-Mathematical Models with Applications ADilations

Dilations Answers

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1
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A square with a side length of 8 units is reduced to a square with a side length of 4 units.

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Triangle JKL is graphed on the coordinate plane.

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J
J'(2, 7),K'(8, 7), and L'(5, 1)
J
J'(–5, 2), K'(5, 2), and L'(0, –5)
J
J'(–3, 2), K'(8, 2), and L'(0, –9)
J
J'(–15, 10), K'(15, 10), and L'(0, –20)
3

A dilation can be used to build a geometric pattern. The graph shows the first three terms of a pattern by applying the same dilation rule to the previous square, starting with the smallest square.

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(5, 5)
(
(7, 7)
(
(8, 8)
(
(16, 16)
4

Which rule represents a dilation with respect to the origin?

A
D1.8(5, 10) = (9, 14)
B
D1.8(5, 10) = (9, 18)
C
D1.8(5, 10) = (13, 18)
D
D1.8(5, 10) = (13, 26)
5

A square with a side length of 2 units is drawn on the coordinate plane with a vertex at the origin. Which shows a dilation of the square by a scale factor of 2?

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Quadrilateral FGHI is dilated with respect to the origin by a scale factor of .

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(−3, 3)
(
(−1, 3)
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(3, −3)
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(3, −1)
7

A rectangular piece of fabric is transformed into a square by cutting the length to match the width.

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A
A dilation was applied to the fabric because the width of the fabric was preserved.
A
A dilation was applied to the fabric because the angle measures were preserved.
A
A dilation was not applied to the fabric because the angle measures are the same.
A
A dilation was not applied to the fabric because the length was changed, not the width.
8

Triangle XYZ is reflected across the y-axis and then dilated.

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In the diagrams, the pre-image is shown with a dashed line and the image is shown with a solid line. Which transformation represents a dilation?

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10

Rita drew the pre-image of circle K with a dashed line and its image after dilation with a solid line. Which shows the dilation of circle K with a scale factor of 2?

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11

Triangle RST is dilated to produce triangle R'S'T.

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A
Its x- and y-coordinates are 2 times the corresponding coordinates of triangle RST.
B
Its x- and y-coordinates are of the corresponding coordinates of triangle RST.
Option B
C
Its x- and y-coordinates are the opposite of the corresponding coordinates of triangle RST.
D
Its x- and y-coordinates are interchanged compared to the coordinates of triangle RST.
12

All circles are similar figures. A single transformation is applied to the circle with center M to create another circle with center N.

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A
A dilation was applied because the center of the circle moved.
B
A dilation was applied because the center of the circle moved.
C
A dilation was applied because the diameter of the circle decreased.
D
A dilation was applied because the diameter of the circle decreased.
E
An isometric transformation was applied because the center of the circle moved.
F
An isometric transformation was applied because the center of the circle moved.
G
An isometric transformation was applied because the diameter of the circle decreased.
H
An isometric transformation was applied because the diameter of the circle decreased.
13

The unit circle has a radius of 1 unit and is centered at the origin. It is dilated so that it passes through the point (4, 0).

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14

Which real-world transformations can be represented by dilations? Select two options.turning a camera to take a photograph cropping a photograph to a square by cutting only one sidereducing a photograph to half its dimensionsenlarging a photograph to double the dimensionsmoving a photograph to a different page

A
turning a camera to take a photograph
B
cropping a photograph to a square by cutting only one side
C
reducing a photograph to half its dimensions
D
enlarging a photograph to double the dimensions
E
moving a photograph to a different page
15

Which statements are true about the figures? Select three options.

A
The factor of dilation is .
Option A
B
The ratio of the perimeter of TRAP to the perimeter of T'R'A'P' is .
Option B
C
The ratio of the x-coordinate of P’ to the x-coordinate of P is .
Option C
D
The ratio of PT to P'T' is .
Option D
E
The ratio of the y-coordinate of R’ to the x-coordinate of R is .
Option E

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