Question

The point P(4, 2) is rotated to become P′(−2, 4) . Describe the rotation by degree and direction.(1 point)
Responses

180°rotation (counter clockwise)
180 degreesrotation (counter clockwise)

90°rotation (counter clockwise)
90 degreesrotation (counter clockwise)

270°rotation (counter clockwise)
270 degreesrotation (counter clockwise)

−90°rotation (clock wise)

Answer 1

To determine the degree and direction of the rotation from point \( P(4, 2) \) to point \( P'(-2, 4) \), we can analyze the transformation geometrically.

1. **Identify the original and new points:**
- Original point \( P(4, 2) \)
- New point \( P'(-2, 4) \)

2. **Visualize the rotation:**
- A 90° rotation counterclockwise around the origin transforms the point \( (x, y) \) to \( (-y, x) \).
- Applying this rule: \( P(4, 2) \) becomes \( P''(-2, 4) \).

3. **Result:**
- Since the transformation matches, we conclude that the rotation from \( P \) to \( P' \) is a **90° rotation counterclockwise**.

Therefore, the correct response is:

**90° rotation (counter clockwise)**.