Question

A rotation maps point A to A’.

On a coordinate plane, point A prime is (negative 3, 4) and A is (3, negative 4).

Which statement describes the rotation?
270° counterclockwise rotation
90° clockwise rotation
180° rotation
90° counterclockwise rotation

Answer 1

To determine the type of rotation that maps point A to A', we can analyze the coordinates of the points involved.

Point A is at (3, -4), and point A' is at (-3, 4).

Let's evaluate the possible rotations:

1. **90° Clockwise Rotation**:
- The coordinates (x, y) will transform to (y, -x).
- For A (3, -4):
- (3, -4) → (-4, -3) (not A’)

2. **90° Counterclockwise Rotation**:
- The coordinates (x, y) will transform to (-y, x).
- For A (3, -4):
- (3, -4) → (4, 3) (not A’)

3. **180° Rotation**:
- The coordinates (x, y) will transform to (-x, -y).
- For A (3, -4):
- (3, -4) → (-3, 4) (This matches A’)

4. **270° Counterclockwise Rotation**:
- The coordinates (x, y) will transform to (-y, x).
- For A (3, -4):
- (3, -4) → (4, 3) (not A’)

Since the only transformation that results in point A' from point A is the **180° rotation**, that is the correct statement.

Thus, the answer is **180° rotation**.