Question

A rotation maps point A(5, 4) to A’(–4, 5).
in which step was an error made

Which describes the rotation?
180° clockwise rotation
180° counterclockwise rotation
90° counterclockwise rotation
90° clockwise rotation

Answer 1

To determine which rotation maps point A(5, 4) to A’(–4, 5), we can analyze each option step by step.

1. **180° clockwise rotation**:
- A point (x, y) rotated 180° around the origin becomes (-x, -y).
- For A(5, 4):
\[
A' = (-5, -4) \quad (\text{not } (–4, 5))
\]
- This is not correct.

2. **180° counterclockwise rotation**:
- Same as 180° clockwise: A(5, 4) becomes (-5, -4).
- This is also not correct.

3. **90° counterclockwise rotation**:
- A point (x, y) rotated 90° counterclockwise around the origin becomes (-y, x).
- For A(5, 4):
\[
A' = (-4, 5) \quad (\text{this matches } (–4, 5))
\]
- This is correct.

4. **90° clockwise rotation**:
- A point (x, y) rotated 90° clockwise around the origin becomes (y, -x).
- For A(5, 4):
\[
A' = (4, -5) \quad (\text{not } (–4, 5))
\]
- This is not correct.

The only accurate option is the **90° counterclockwise rotation**, which maps point A(5, 4) to A’(–4, 5). Thus, there was no error made in regard to the calculation of a 90° counterclockwise rotation.