AnswersFL-1205070-MJ Grade 8 Pre-Algebra BRotations in the Coordinate Plane

Rotations in the Coordinate Plane Answers

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Sample Response/Explanation: There are 360 degrees in one revolution, so a 270-degree clockwise rotation would be the same as a 90-degree counterclockwise rotation. Therefore, the rule would be to map (x, y) to (–y, x). Which did you include in your response? Check all that apply.There are 360 degrees in one revolution.xA 270-degree clockwise rotation is the same as a 90-degree counterclockwise rotation.(x, y) maps to (–y, x).

A
There are 360 degrees in one revolution.x
B
A 270-degree clockwise rotation is the same as a 90-degree counterclockwise rotation.
C
(x, y) maps to (–y, x).
3

What is the mapping rule for a 180° rotation?

A
(x, y) → (y, x)
B
(x, y) → (–y, x)
C
(x, y) → (y, –x)
D
(x, y) → (–x, –y)
4

Find the coordinates of point A’.

A
A’(2, 3)
B
A’(–3, –2)
C
A’(–2, –3)
D
A’(–2, 3)
5

What are the coordinates of G’?

A
G’(–2, –2)
B
G’(–4,–2)
C
G’(2, –4)
D
G’(4, 2)
6

What are the coordinates of its image V’?

A
V’(1, 4)
B
V’(–1, 4)
C
V’(–1, –4)
D
V’(4, 1)
7

What are the coordinates of the image of point F?

A
(5, –3)
B
(5, 3)
C
(–5, –3)
D
(3, –5)
8

What is the correct set of image points for triangle A’B’C’?

A
A’(3, 2), B’(3, 5), C’(2, 4)
B
A’(3, –2), B’(3, –5), C’(2, –4)
C
A’(–3, –2), B’(–3, –5), C’(–2, –4)
D
A’(–3, 2), B’(–3, 5), C’(–2, 4)
9

Which describes the rotation?

A
180° clockwise rotation
B
180° counterclockwise rotation
C
90° counterclockwise rotation
D
90° clockwise rotation
11

✔ an error in step 1an error in step 2an error in step 3no error.

A
✔ an error in step 1
B
an error in step 2
C
an error in step 3
D
no error
12

Based on what you know about rotations, what do you think the mapping rule is for a rotation of 270 degrees clockwise? Explain.

Answer:

A rotation of 270 degrees clockwise is equivalent to a 90-degree counterclockwise rotation. Since there are 360 degrees in a full circle, 360 - 270 = 90. Therefore, the mapping rule for a 270-degree clockwise rotation is (x, y) → (–y, x).

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