Question

Which rotation maps point K(8, –6) to K’(–6, –8)?
180° counterclockwise rotation
90° clockwise rotation
90° counterclockwise rotation
180° clockwise rotation

Answer 1

To determine which rotation maps point \( K(8, -6) \) to point \( K'(-6, -8) \), we can analyze the transformations based on rotation angles around the origin.

1. **90° clockwise rotation**:
The formula is:
\[
(x, y) \to (y, -x)
\]
Applying this to \( K(8, -6) \):
\[
(8, -6) \to (-6, -8)
\]
This matches \( K'(-6, -8) \).

2. **90° counterclockwise rotation**:
The formula is:
\[
(x, y) \to (-y, x)
\]
Applying this to \( K(8, -6) \):
\[
(8, -6) \to (6, 8)
\]
This does not match \( K'(-6, -8) \).

3. **180° clockwise rotation**:
The formula is:
\[
(x, y) \to (-x, -y)
\]
Applying this to \( K(8, -6) \):
\[
(8, -6) \to (-8, 6)
\]
This does not match \( K'(-6, -8) \).

4. **180° counterclockwise rotation**:
This is the same as the clockwise rotation:
\[
(8, -6) \to (-8, 6)
\]
This does not match \( K'(-6, -8) \).

Based on the calculations, the correct rotation that maps \( K(8, -6) \) to \( K'(-6, -8) \) is the **90° clockwise rotation**.