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Rotations Answers

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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°
2
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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
3

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)
4

Which shows the pre-image of quadrilateral W'X'Y'Z' before the figure was rotated according to the rule (x, y) → (–x, –y)?

Question illustration
A
On a coordinate plane, a quadrilateral has points W (negative 3, 2), X (negative 3, 6), Y (negative 4, 6), Z (negative 5, 3).
Option A
B
On a coordinate plane, a quadrilateral has points W (3, negative 2), X (3, negative 6), Y (4, negative 6), Z (5, negative 3).
Option B
C
On a coordinate plane, a quadrilateral has points W (negative 2, negative 3), X (negative 6, negative 3), Y (negative 6, negative 4), Z (negative 3, negative 5).
Option C
D
On a coordinate plane, a quadrilateral has points W (negative 3, negative 2), X (negative 3, negative 6), Y (negative 4, negative 6), Z (negative 5, negative 3).
Option D
5

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)
6

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°
7

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)
8

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)
9

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)
10

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.

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