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)Responses90 degrees (counterclockwise)90 degrees (counterclockwise)−90 degrees (clockwise)negative 90 degrees (clockwise)270 degrees (counterclockwise)270 degrees (counterclockwise)−180 degrees (clockwise) or 180 degrees (counterclockwise)

Answer 1

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

For a point \( (x, y) \), the standard rotation mappings about the origin are:

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

Now let’s analyze the transformation that takes \( P(-4, 10) \) to \( P'(-10, -4) \):

1. Starting point \( P(-4, 10) \):
- After 90 degrees counterclockwise:
\[
(-10, -4) \quad (this is P')
\]
Thus, applying the mapping confirms:

\[
P(-4, 10) \rightarrow (-10, -4) \text{ after a rotation of } 90 \text{ degrees counterclockwise.}
\]

Since the transformation from \( P \) to \( P' \) matches the 90 degrees counterclockwise mapping, the answer is:

**90 degrees (counterclockwise)**.