AnswersDL Geometry AUnit Test

Rotations Answers

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1
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For the transformation to be defined as a rotation, which statements must be true? Select three options.

A
The segment connecting the center of rotation, C, to a point on the pre-image (figure 1) is equal in length to the segment that connects the center of rotation to its corresponding point on the image (figure 2).
B
The transformation is rigid.
C
Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2.
D
Segment CP is parallel to segment CP'.
E
If figure 1 is rotated 180° about point C, it will be mapped onto itself.
2
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Which statements are true regarding the transformation? Select three options.

A
The rule for the transformation is (x, y) → (–x, –y).
B
The coordinates of L' are (–2,–2).
C
The coordinates of M' are (–4,4).
D
The coordinates of N' are (6,–1).
E
The coordinates of N' are (–1,–6).
3

Which rules could describe the rotation? Select two options.

A
R0, 90°
B
R0, 180°
C
R0, 270°
D
(x, y) → (–y, x)
E
(x, y) → (–x, –y)
4

Triangle ABC was transformed using the rule (x, y) → (–y, x). The vertices of the triangles are shown.A (–1, 1)B (1, 1)C (1, 4) A' (–1, –1)B' (–1, 1)C' (–4, 1)

A
The transformation was a 90° rotation about the origin.
B
The transformation was a 180° rotation about the origin.
C
The transformation was a 270° rotation about the origin.
D
The transformation was a 360° rotation about the origin.
5

On a coordinate plane, a trapezoid has points H prime (negative 3, negative 2), J prime (negative 2, negative 3), K prime (negative 3, negative 4), G prime (negative 5, negative 2).

Question illustration
A
(2, 3)
B
(–2, 3)
C
(3, 2)
D
(3, –2)
6

Parallelogram ABCD is rotated to create image A'B'C'D'.

Question illustration
A
(x, y) → (y, –x)
B
(x, y) → (–y, x)
C
(x, y) → (–x, –y)
D
(x, y) → (x, –y)
7

Which transformations could have taken place? Select two options.

A
R0, 90°
B
R0, 180°
C
R0, 270°
D
R0, –90°
E
R0, –180°
8

Which transformations could have taken place? Select two options. Consider both clockwise and counterclockwise rotations when answering this question.

A
R0, 90°
B
R0, 180°
C
R0, 270°
D
R0, –90°
E
R0, –270°
9

Which shows the image of ΔRST after the rotation (x, y) → (y, –x)?

Question illustration
A
On a coordinate plane, a triangle has points R prime (1, 2), S prime (3, negative 1), T prime (7, 1).
Option A
B
On a coordinate plane, a triangle has points R prime (1, negative 2), S prime (3, 1), T prime (7, negative 1).
Option B
C
On a coordinate plane, a triangle has points R prime (negative 1, negative 2), S prime (negative 3, 1), T prime (negative 7, negative 1).
Option C
D
On a coordinate plane, a triangle has points R prime (2, 1), S prime (negative 1, 3), T prime (1, 7).
Option D
10

A pentagon is transformed according to the rule R0, 180°. Which is another way to state the transformation?

A
(x, y) → (–x, –y)
B
(x, y) → (–y –x)
C
(x, y) → (x, –y)
D
(x, y) → (–x, y)
11

Which shows the image of quadrilateral ABCD after the transformation R0, 90°?

Question illustration
A
On a coordinate plane, a rectangle has points A prime (0, negative 1), B prime (1, 0), C prime (3, negative 2), D prime (2, negative 3).
Option A
B
On a coordinate plane, a rectangle has points A prime (0, 1), B prime (0, negative 1), C prime (negative 3, 2), D prime (negative 2, 3).
Option B
C
On a coordinate plane, a rectangle has points A prime (0, negative 1), B prime (negative 1, 0), C prime (negative 3, negative 2), D prime (negative 2, negative 3).
Option C
D
On a coordinate plane, a rectangle has points A prime (1, 0), B prime (0, 1), C prime (2, 3), D prime (3, 2).
Option D
12

A triangle has vertices at R(1, 1), S(–2, –4), and T(–3, –3). The triangle is transformed according to the rule R0, 270°. What are the coordinates of S'?

A
(–4, 2)
B
(–2, 4)
C
(2, 4)
D
(4, –2)
13

Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown.R (1, 1)S (3, 1)T (1, 6) R' (–1, –1)S' (–3, –1)T' (–1, –6)

A
The transformation was a 90° rotation about the origin.
B
The transformation was a 180° rotation about the origin.
C
The transformation was a 270° rotation about the origin.
D
The transformation was a 360° rotation about the origin.
14

Triangle XYZ has vertices X(1, 3), Y(0, 0), and Z(–1, 2). The image of triangle XYZ after a rotation has verticesX'(–3, 1), Y'(0, 0), and Z'(–2, –1). Which rule describes the transformation?

A
R0, 90°
B
R0, 180°
C
R0, 270°
D
R0, 360°
15

A triangle is rotated 90° about the origin. Which rule describes the transformation?

A
(x, y) → (–x, –y)
B
(x, y) → (–y, x)
C
(x, y) → (–y, –x)
D
(x, y) → (y, –x)
16

Quadrilateral ABCD is transformed according to the rule (x, y) → (y, –x). Which is another way to state the transformation?

A
R0, 90°
B
R0, 180°
C
R0, 270°
D
R0, 360°

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