Question

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

−270°
rotation (clockwise)
negative 270 degrees rotation (clockwise)

180°
rotation (counter clockwise)
180 degrees rotation (counter clockwise)

−90°
rotation (clockwise)
negative 90 degrees rotation (clockwise)

90°
rotation (counter clockwise)
90 degrees rotation (counter clockwise)

Answer 1

To determine the rotation of the point \( P(4, 2) \) to the point \( P'(-2, 4) \), we can analyze the transformation geometric.

1. **Find the center of rotation**:
A common way to visualize this is to consider a rotation around the origin or another point. In this case, since the coordinates of point P change from (4, 2) to (-2, 4), we can observe the changes in the x and y coordinates to help infer the angle and direction of the rotation.

2. **Vector analysis**:
- The vector from the origin to the point P is \( (4, 2) \).
- The vector from the origin to point P' is \( (-2, 4) \).

3. **Visualizing the points**:
- Point P is located in the first quadrant (4, 2).
- Point P' is located in the second quadrant (-2, 4).

4. **Identifying the rotation**:
- To derive the rotation, we can compare the coordinates `(x, y)`.
- Rotating \( P(4, 2) \) by 90 degrees counterclockwise, we can use the rule \( (x, y) \to (-y, x) \):
- For \( (4, 2) \):
- \( (4, 2) \) becomes \( (-2, 4) \).

Thus, \( P \) rotates to \( P' \) when rotated 90 degrees counterclockwise.

Therefore, the correct description of the rotation is:

**90° rotation (counter clockwise)** or **90 degrees rotation (counter clockwise)**.