Question

The point P(-1,2) is rotated to be one P'(2,1). Describe the rotation by degree and direction.
-270 degree rotation
180 degree rotation
-90 degree rotation
90 degree rotation

Answer 1

To determine the rotation that transforms the point \( P(-1, 2) \) to \( P'(2, 1) \), we can analyze the positions of the points and the transformations involved.

1. **Calculate the difference in coordinates**:
\[
P' - P = (2 - (-1), 1 - 2) = (3, -1)
\]

2. **Based on the rotation options** below are the implications of various rotations:

- **90 degree rotation**:
A 90-degree rotation counter-clockwise around the origin transforms a point \( (x, y) \) to \( (-y, x) \).

- **-90 degree rotation (or 270 degree rotation clockwise)**:
A -90-degree rotation transforms a point \( (x, y) \) to \( (y, -x) \).

- **180 degree rotation**:
A 180-degree rotation transforms a point \( (x, y) \) to \( (-x, -y) \).

- **-270 degree rotation (or 90 degrees rotation clockwise)**:
This is essentially the same as the -90 degrees rotation.

3. **Identify the transformation**:
We will examine the original point \( P(-1, 2) \) and apply possible rotations to see which one lands us at \( P'(2, 1) \).

**Using the 90-degree rotation**:
\[
P(-1, 2) \to (-2, -1) \quad \text{(not } P'(2, 1) \text{)}
\]

**Using the -90 degree rotation**:
\[
P(-1, 2) \to (2, 1) \quad \text{(this matches } P'(2, 1) \text{)}
\]

**Using the 180-degree rotation**:
\[
P(-1, 2) \to (1, -2) \quad \text{(not } P'(2, 1) \text{)}
\]

**Using the -270 degree rotation**:
This is equivalent to a 90-degree clockwise rotation, which we have already established corresponds to the same result as the -90 degree rotation.

Given this, the correct rotation that transforms point \( P(-1, 2) \) to \( P'(2, 1) \) is:

**-90 degree rotation (or 270 degree clockwise rotation)**.