Question
Rotations as Functions Quick Check 2 of 52 of 5 Items Question A point is rotated about the origin. Its coordinates are P(−4,10) and P′(−10,−4) . Determine the degree of rotation and direction by applying rotation mapping.(1 point) Responses 90 degrees (counterclockwise) 90 degrees (counterclockwise) −90 degrees (clockwise) negative 90 degrees (clockwise) 270 degrees (counterclockwise) 270 degrees (counterclockwise) −180 degrees (clockwise) or 180 degrees (counterclockwise) negative 180 degrees (clockwise) or 180 degrees (counterclockwise) Skip to navigation page 15 of 15 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.
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GPT-4o mini
To determine the degree of rotation and the direction for the point P(−4,10) to P′(−10,−4), we can analyze the coordinates based on rotation transformations.
The general rotation rules around the origin (0, 0) in the coordinate plane are as follows:
- A 90-degree counterclockwise rotation takes a point (x, y) to (-y, x).
- A 180-degree rotation takes a point (x, y) to (-x, -y).
- A 270-degree counterclockwise rotation takes a point (x, y) to (y, -x).
- A -90-degree (clockwise) rotation takes a point (x, y) to (y, -x).
Given P(−4, 10):
- After a **90-degree counterclockwise rotation**, it would become (-10, -4), which matches P′(−10, −4).
- A **-90-degree clockwise rotation** would take it to (10, 4), which does not match P′.
Thus, the correct response is:
**90 degrees (counterclockwise)**.
The general rotation rules around the origin (0, 0) in the coordinate plane are as follows:
- A 90-degree counterclockwise rotation takes a point (x, y) to (-y, x).
- A 180-degree rotation takes a point (x, y) to (-x, -y).
- A 270-degree counterclockwise rotation takes a point (x, y) to (y, -x).
- A -90-degree (clockwise) rotation takes a point (x, y) to (y, -x).
Given P(−4, 10):
- After a **90-degree counterclockwise rotation**, it would become (-10, -4), which matches P′(−10, −4).
- A **-90-degree clockwise rotation** would take it to (10, 4), which does not match P′.
Thus, the correct response is:
**90 degrees (counterclockwise)**.
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