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

Question

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

Answer 1

To determine the rotation of point P (-1, 2) to point P' (2, 1), we can analyze the transformation by calculating the angles involved.

1. Original Point: P(-1, 2)

   • Coordinates: \((-1, 2)\)

2. New Point: P'(2, 1)

   • Coordinates: \((2, 1)\)

Step 1: Determine the center of rotation

We can check the coordinates of the original and new points to find a likely center of rotation. In this case, we can calculate the midpoints to find a center of rotation if needed.

Step 2: Calculate the transformation

Since the coordinates change as follows:

• From (-1, 2) to (2, 1), the x-coordinate increases by 3 and the y-coordinate decreases by 1.

Step 3: Check the angles

We can visually assess the rotation:

• The original point (-1, 2) is in the second quadrant (x negative, y positive).
• The new point (2, 1) is in the first quadrant (x positive, y positive).

By evaluating the changes in coordinates, we observe the direction of the rotation:

• When rotating a point \((x, y)\) by 90 degrees counterclockwise around the origin, the coordinates become \((-y, x)\).
• A rotation of 90 degrees clockwise would transform the coordinates as follows: \((y, -x)\).

In this case, if we examine our specific points:

• Translating P(-1,2) under a 90-degree clockwise rotation yields the point (2, 1).

Conclusion

The correct answer is:

D. -90 degree rotation (clockwise rotation by 90 degrees turns P into P').