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

Question

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).