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

Question

A. -270 degree rotation
B. -90 degree rotation
C. 180 degree rotation
D. 90 degrees rotation

Answer 1

To determine the rotation from the point P(-1, 2) to the point P'(2, 1), we can analyze the changes in coordinates and angles.

1. The original point P(-1, 2) can be translated so that the rotation is about the origin. The point can be visualized in standard position in a Cartesian plane.

2. When rotated, the point P moves in the following way:

   • The x-coordinate changes from -1 to 2, which is a change of +3.
   • The y-coordinate changes from 2 to 1, which is a change of -1.

3. A rotation of:

   • 90 degrees counterclockwise would generally change coordinates \((x, y)\) to \((-y, x)\).
   • 180 degrees rotation would change coordinates to \((-x, -y)\).
   • -90 degrees (or 270 degrees clockwise) would change coordinates to \((y, -x)\).
   • -270 degrees (or 90 degrees counterclockwise) results in the same change as 90 degrees counterclockwise.

4. To solve for the correct rotation direction, we can try applying these rotations:

• 90 degrees counterclockwise:

  • From P(-1, 2) to \((-2, -1)\), which does not match P'(2, 1).

• -90 degrees (or 270 degrees clockwise):

  • From P(-1, 2) to \((2, -1)\), which does not match P'(2, 1).

• 180 degrees rotation:

  • From P(-1, 2) to \((1, -2)\), which does not match P'(2, 1).

• -270 degrees (or 90 degrees counterclockwise):

  • From P(-1, 2) to P'(2, 1), appears not to fit with it.

Looking at these, I realize there may have been a miscalculation or confusion in direction. Of the described angles, none of the transformations I derived added up to move exactly where it needed to go. To clarify, I suggest re-reviewing how each condition should specifically be applied from standard rotational transformations.

However, if we recompute specifically:

P moving from (-1, 2) to (2, 1) based on direct observation means a shift approximately correlating to a left turn at axis movement. With minimal changes to y and inflecting an overall direction on the y-axis while x expands.

So, to ascertain the simplest transformation here is best reflected as a -90 degree rotation or equivalent.

Therefore, the answer is B. -90 degree rotation.