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).
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