Question

Rotate the point (-5,8) around the origin 270 degrees counterclockwise. State the coordinates of the point.

A. (5, -8)
B. (-8, -5)
C. (8, -5)
D. (8, 5)

Answer 1

After rotating the point (-5, 8) 270 degrees counterclockwise around the origin, the new coordinates are (8, 5), making the correct answer D. (8, 5).

Step-by-step explanation:

To rotate the point (-5, 8) around the origin 270 degrees counterclockwise, we will use the rules for 90-degree rotations. A 270-degree counterclockwise rotation is equivalent to three consecutive 90-degree counterclockwise rotations. The rules for a single 90-degree counterclockwise rotation about the origin are to swap the x and y values of the point and to change the sign of the new x-coordinate. Therefore:

1. First 90-degree rotation changes (-5, 8) to (-8, -5).
2. Second 90-degree rotation changes (-8, -5) to (5, -8).
3. Third 90-degree rotation changes (5, -8) to (8, 5).

The coordinates of the point after a 270-degree counterclockwise rotation are (8, 5). Therefore, the correct answer is D. (8, 5).