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)

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

1. **Find the angle of rotation in terms of the coordinates:**
- The original point is \( P(-4, 10) \).
- The new point is \( P'(-10, -4) \).

2. **Using formulas for rotation:**
The general formula for a 90-degree counterclockwise rotation about the origin is:
\[
(x, y) \rightarrow (-y, x)
\]
A 180-degree rotation converts:
\[
(x, y) \rightarrow (-x, -y)
\]
A 270-degree counterclockwise (or 90-degree clockwise) rotation translates to:
\[
(x, y) \rightarrow (y, -x)
\]
And a 90-degree clockwise rotation translates to:
\[
(x, y) \rightarrow (y, -x)
\]

3. **Check transformations:**
- **90 degrees counterclockwise:**
\[
P(-4, 10) \rightarrow P''(-10, -4) \text{ (This yields } P'(-10, -4)\text{)}
\]
- **180 degrees:**
\[
P(-4, 10) \rightarrow P''(4, -10) \text{ (Not equal to } P'\text{)}
\]
- **90 degrees clockwise:**
\[
P(-4, 10) \rightarrow P''(10, 4) \text{ (Not equal to } P'\text{)}
\]
- **270 degrees counterclockwise:**
\[
P(-4, 10) \rightarrow P''(10, -4) \text{ (Not equal to } P'\text{)}
\]

From our calculations, we can see that the point \( P \) was transformed to \( P' \) by a **90 degrees counterclockwise rotation**.

So the correct answer is:

**90 degrees (counterclockwise)**