Final answer:
To match the pre-image and its clockwise rotation with the coordinates of its image, we perform 90°, 180°, and 270° rotations around the origin. The rotation alters the coordinates depending on the angle, swapping them and changing signs as necessary to determine the resulting location on the coordinate plane.
Step-by-step explanation:
The question involves finding the coordinates of a point after it has been rotated around the origin in a clockwise direction. The rotations specified are 90°, 180°, and 270°. Let's go through these rotations step-by-step.
- A 90° clockwise rotation will swap the coordinates and change the sign of the former y-coordinate. So, the point (5, -2) becomes (2, 5).
- A 180° rotation reverses both coordinates, turning (2, -5) into (-2, 5) and (-5, 2) into (5, -2).
- Finally, a 270° clockwise rotation (equivalent to a 90° counterclockwise rotation) will swap the coordinates and change the sign of the new y-coordinate, which results in turning (-2, 5) into (5, 2) and (5, 2) into (-2, -5).
Therefore, the correctly matched pairs for the question are:
- (5, -2) rotated 90° clockwise is (2, 5)
- (2, -5) rotated 180° clockwise is (5, 2)
- (2, 5) rotated 270° clockwise is (-5, -2)
- (-5, 2) rotated 90° clockwise is (-2, 5)
- (-2, 5) rotated 180° clockwise is (5, -2)
- (-2, -5) rotated 270° clockwise is (5, 2)