Which of the following mappings is used for a 270-degree (counterclockwise) rotation?(1 point)

Question

Responses

1 (x,y)→(−y,x)

2 (x,y)→(−y,−x)

3 (x,y)→(y,−x)

4 NONE

Answer 1

To determine the mapping for a 270-degree counterclockwise rotation, we can analyze how the coordinates change during this rotation.

When rotating a point (x, y) 270 degrees counterclockwise around the origin, the transformation can be derived as follows:

1. A 90-degree counterclockwise rotation transforms the point (x, y) to (-y, x).
2. A 180-degree rotation transforms it to (-x, -y).
3. A 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation, which transforms the point (x, y) to (y, -x).

Therefore, the correct mapping for a 270-degree (counterclockwise) rotation is:

3. (x, y) → (y, -x)

So the answer is 3 (x,y)→(y,−x).