Question

A point is rotated about the origin. Its coordinates are P(−4,10) and P′(−10,−4). Determine the degree of rotation and direction by applying rotation mapping.(1 point)%0D%0AResponses%0D%0A%0D%0A90 degrees (counterclockwise)%0D%0A90 degrees (counterclockwise)%0D%0A%0D%0A270 degrees (counterclockwise)%0D%0A270 degrees (counterclockwise)%0D%0A%0D%0A−180 degrees (clockwise) or 180 degrees (counterclockwise)%0D%0Anegative 180 degrees (clockwise) or 180 degrees (counterclockwise)%0D%0A%0D%0A−90 degrees (clockwise)

Answer 1

To find the degree and direction of rotation of point \( P(-4, 10) \) to point \( P'(-10, -4) \), we can use rotation formulas or analyze the transformation directly.

1. **Identify the coordinates**:
- \( P(-4, 10) \)
- \( P'(-10, -4) \)

2. **Check for common rotation angles**:
- The standard rotation transformations are as follows:
- \( 90^\circ \) counterclockwise: \( (x, y) \) becomes \( (-y, x) \)
- \( 180^\circ \) (either direction): \( (x, y) \) becomes \( (-x, -y) \)
- \( 270^\circ \) counterclockwise (or \( 90^\circ \) clockwise): \( (x, y) \) becomes \( (y, -x) \)

3. **Applying transformations**:
- **Check for \( 90^\circ \) counterclockwise**:
- \( P(-4, 10) \) would transform to \( (-10, -4) \),
- which matches \( P'(-10, -4) \).
- **Therefore**, the rotation from \( P \) to \( P' \) is \( 90^\circ \) counterclockwise.

Thus, the answer is **90 degrees (counterclockwise)**.