Question

The point P (4,2) is rotate to become P' (-2,4). Describe the rotation by degree and direction.

a. 180 degree rotation
b. -90 degree rotation
c. 90 degree rotation
d. -270 degree rotation

Answer 1

To determine the rotation that takes point P (4, 2) to point P' (-2, 4), we can analyze the coordinates.

1. A **90-degree clockwise rotation** moves a point (x, y) to (y, -x). Let's see if this holds true:
- Apply 90-degree clockwise rotation to P (4, 2):
- (y, -x) = (2, -4).

This does not yield P'.

2. A **90-degree counterclockwise rotation** moves a point (x, y) to (-y, x):
- Apply 90-degree counterclockwise rotation to P (4, 2):
- (-y, x) = (-2, 4).

This matches P', indicating that a 90-degree counterclockwise rotation is indeed the transformation.

Thus, P (4, 2) rotated to P' (-2, 4) is:

**Answer: c. 90 degree rotation (counterclockwise direction)**.