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

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

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

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').**