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) Responses 90 degrees (counterclockwise) 90 degrees (counterclockwise) 270 degrees (counterclockwise) 270 degrees (counterclockwise) −90 degrees (clockwise) negative 90 degrees (clockwise) −180 degrees (clockwise) or 180 degrees (counterclockwise)

Answer 1

To determine the degree of rotation and the direction, we can analyze the transformation of the point \( P(-4, 10) \) to \( P'(-10, -4) \).

A rotation about the origin can be characterized by the following coordinate transformations for a point \( (x, y) \):

- **90 degrees counterclockwise**: \( (x, y) \to (-y, x) \)
- **180 degrees**: \( (x, y) \to (-x, -y) \)
- **270 degrees counterclockwise (or equivalently, 90 degrees clockwise)**: \( (x, y) \to (y, -x) \)

Let's check the transformation needed to go from \( P(-4, 10) \) to \( P'(-10, -4) \):

1. **Check 90 degrees counterclockwise**:
\[
(-4, 10) \to (-10, -4)
\]
Here, the transformation would give \( ( -y, x ) \to (-10, -4)\) which matches \( P' \). This indicates a 90 degrees counterclockwise rotation.

Now, we can conclude that the point \( P(-4, 10) \) is rotated to \( P'(-10, -4) \) by **90 degrees counterclockwise**.

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