AnswersPMHS Geometry Q2Using Triangle Congruence Theorems

Dilations in the Coordinate Plane Answers

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1
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What is the scale factor in the dilation?

Question illustration
A
One-sixth
Option A
B
One-third
Option B
C
3
D
6
2
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What is true about the dilation?

Question illustration
A
It is a reduction with a scale factor between 0 and 1.
B
It is a reduction with a scale factor greater than 1.
C
It is an enlargement with a scale factor between 0 and 1.
D
It is an enlargement with a scale factor greater than 1.
3

The rectangle is the image after a dilation with the center of dilation at the origin of rectangle ABCD. The pre-image of , point A, has coordinates of (–4, 3.2). What is the scale factor of the dilation and what are the coordinates of point C?

Question illustration
A
The scale factor is 2.5 and the coordinates of point C are (–2.4, –0.8).
B
The scale factor is 0.4 and the coordinates of point C are (–2.4, –0.8).
C
The scale factor is 2.5 and the coordinates of point C are (–15, 5).
D
The scale factor is 0.4 and the coordinates of point C are (–15, 5).
4

What are the coordinates of the image of point A after the segment has been dilated by a scale factor of with a center of dilation at the origin?

Question illustration
A
(–2, 1)
B
(1, –2)
C
(Negative one-half, 1)
Option C
D
(1, negative one-half)
Option D
5

Which figure could be the result of dilating this rectangle with a scale factor between 0 and 1?

Question illustration
A
On a coordinate plane, a rectangle has points (0, 0), (0, 1), (2, 0), (2, 1).
Option A
B
On a coordinate plane, a rectangle has points (0, 0), (0, 4), (8, 4), (8, 0).
Option B
C
On a coordinate plane, a rectangle has points (0, 0), (0, 1), (4, 1), (4, 0).
Option C
D
On a coordinate plane, a rectangle has points (0, 0), (0, 2), (8, 2), (8, 0).
Option D
6

What is true about the dilation?

Question illustration
A
It has a scale factor between zero and one and is a reduction.
B
It has a scale factor greater than one and is a reduction.
C
It has a scale factor between zero and one and is an enlargement.
D
It has a scale factor greater than one and is an enlargement.
7

A quadrilateral with vertices at A(4, –4), B(4, –16), C(12, –16), and D(12, –4) has been dilated with a center at the origin. The image of D, point , has coordinates (36, –12). What is the scale factor of the dilation?

Question illustration
A
StartFraction 1 Over 9 EndFraction
Option A
B
One-third
Option B
C
3
D
9
8

The graph shows an image of a dilation about the origin with a scale factor of .What are the coordinates of the pre-image of , point A?

Question illustration
A
(–8, –12)
B
(–12, –8)
C
(–2, –3)
D
(–3, –2)
9

Segment AB is being dilated with the center at the origin. The image of A, point , has coordinates of (3.2, 6.4). What is the scale factor of the dilation and the coordinates of point ?

Question illustration
A
The scale factor is 0.8 and the coordinates of point are (–3.2, –4.8).
Option A
B
The scale factor is 1.25 and the coordinates of point are (–3.2, –4.8).
Option B
C
The scale factor is 0.8 and the coordinates of point are (–5, –7.5).
Option C
D
The scale factor is 1.25 and the coordinates of point are (–5, –7.5).
Option D
10

Which graph shows the result of dilating this figure by a factor of about the origin?

Question illustration
A
On a coordinate plane, triangle A prime B prime C prime has points (negative 2, 2), (2, 2), (2, negative 2).
Option A
B
On a coordinate plane, triangle A prime B prime C prime has points (negative 3, 3), (3, 3), (3, negative 3).
Option B
C
On a coordinate plane, triangle A prime B prime C prime has points (Negative 18, 18), (18, 18), (18, negative 18).
Option C
D
On a coordinate plane, triangle A prime B prime C prime has points (negative 12, 12), (12, 12), (12, negative 12).
Option D

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