Question

A figure is rotated 90 degrees counterclockwise about the origin. Which of the following function mappings was applied?
1. (x,y) to (y,-x)
2. (x,y) to (-y,x)
3. (x,y) to (-x,-y)
4. (x,y) to (y,x)

Answer 1

To determine which function mapping corresponds to a 90-degree counterclockwise rotation about the origin, let's analyze each mapping option.

1. **(x,y) to (y,-x)**:
- This would rotate the point (x, y) to (y, -x), which is not a 90-degree counterclockwise rotation.

2. **(x,y) to (-y,x)**:
- This mapping transforms (x, y) to (-y, x). This corresponds to a 90-degree counterclockwise rotation about the origin.

3. **(x,y) to (-x,-y)**:
- This mapping reflects the point over the origin, which is a 180-degree rotation, not a 90-degree rotation.

4. **(x,y) to (y,x)**:
- This mapping swaps the coordinates (x, y) to (y, x). This is not a rotation.

Based on this analysis, the correct mapping for a 90-degree counterclockwise rotation about the origin is option **2: (x,y) to (-y,x)**.