The point P (−1,2) is rotated to become P′ (2,1) . Describe the rotation by degree and direction.(1 point) Responses 180° rotation 180 degrees rotation 90° rotation 90 degrees rotation −90° rotation negative 90 degrees rotation −270° rotation

Answer 1

To determine the rotation that transforms point P (−1, 2) to point P′ (2, 1), we can analyze the movement of the point.

Original point: P (−1, 2)
Transformed point: P′ (2, 1)

We can analyze this by checking the coordinates. A rotation of 90° (counter-clockwise) around the origin for point P would give us:

1. From P (−1, 2):

   • After a 90° rotation counter-clockwise, the coordinates transform as follows:
   • New x = -y (which is -2)
   • New y = x (which is -1)
   • Resulting in point (-2, -1), which does not match P′.

2. Testing for 180°:

   • After a 180° rotation, the coordinates transform:
   • New x = -x (which is 1)
   • New y = -y (which is -2)
   • Resulting in point (1, -2), which also does not match P′.

3. Testing for 90° (clockwise):

   • New x = y (which is 2)
   • New y = -x (which is 1)
   • Resulting in point (2, -(-1)) = (2, 1), which matches P′.

Thus, the transformation from P to P′ is a 90-degree clockwise (or -90 degrees) rotation.

The answer is −90° rotation (or negative 90 degrees rotation).