The point P (-1,2) is rotated to become P' (2,1). Describe the rotation by degree and direction.

Question

(1 point)
0-270°
rotation
• 180° rotation
• -90° rotation
• 90° rotation

Answer 1

To determine the rotation of point P (-1, 2) to P' (2, 1), we can analyze the change in coordinates.

1. Identify the original and new points:

   • P = (-1, 2)
   • P' = (2, 1)

2. Calculate the movement:

   • The x-coordinate changes from -1 to 2 (which is an increase of 3).
   • The y-coordinate changes from 2 to 1 (which is a decrease of 1).

3. Visualize the rotation:

   • We can visualize this transformation in a coordinate system.
   • The point P is in the second quadrant (where x is negative and y is positive).
   • The point P' is in the first quadrant (where both x and y are positive).

4. Identify the rotation direction:

   • A 90° rotation counterclockwise (or -270°) moves a point (x, y) to (-y, x).
   • A 90° rotation clockwise (or 270°) moves a point (x, y) to (y, -x).
   • A 180° rotation moves a point (x, y) to (-x, -y).

5. Check the transformation:

   • If we apply a 90° rotation clockwise to point P (-1, 2):
     • The new coordinates would be (2, 1), which matches point P'.

Thus, the correct description of the rotation is: 90° rotation clockwise (or -270° rotation counterclockwise).

Since the options provided include "90° rotation," that is the answer.