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
-270 rotation

Answer 1

To determine the rotation that transforms point P (-1, 2) into point P' (2, 1), we can use coordinate manipulation.

1. Calculate the rotation angle:

   We start by identifying the original and new positions of the points:

   • Point P: (-1, 2)
   • Point P': (2, 1)

2. Visual representation:

   • The coordinates indicate that the point P is located 1 unit left and 2 units up from the origin (0,0).
   • Point P' is located 2 units right and 1 unit up from the origin.

3. Determine the transformation:

   To see how P is transformed to P', we can consider rotating about the origin.

   • The translation from P to P' in terms of x-coordinates:
     • From -1 to 2: This is a move of 3 units to the right.
   • The translation in terms of y-coordinates:
     • From 2 to 1: This is a move of 1 unit down.

4. Analyzing the rotation:

   If we consider the 90° clockwise rotation:

   • The new coordinates can be calculated for a 90° clockwise rotation using the formula (x', y') = (y, -x).
   • So, if we rotate P (-1, 2):
     • x' = y = 2
     • y' = -x = -(-1) = 1
   • Therefore, (x', y') becomes (2, 1), which is exactly point P'.

Thus, we can conclude:

The rotation is 90° clockwise.