Question

Tanya’s rotation maps point K(24, –15) to K’(–15, –24). Which describes the rotation?
90 degrees clockwise rotation
270 degrees clockwise rotation
180 degrees rotation
90 degrees counterclockwise rotation

Answer 1

To determine the type of rotation that maps point \( K(24, -15) \) to point \( K'(-15, -24) \), we can analyze how the coordinates change under different rotations.

1. **90 Degrees Clockwise Rotation:**
The transformation for a 90-degree clockwise rotation about the origin is given by:
\[
(x, y) \to (y, -x)
\]
Applying this to point \( K(24, -15) \):
\[
(24, -15) \to (-15, -24)
\]
This matches point \( K' \).

2. **270 Degrees Clockwise Rotation:**
A 270-degree clockwise rotation is equivalent to a 90-degree counterclockwise rotation. Its transformation is:
\[
(x, y) \to (-y, x)
\]
Applying it:
\[
(24, -15) \to (15, 24)
\]
This does not match \( K' \).

3. **180 Degrees Rotation:**
The transformation for a 180-degree rotation is:
\[
(x, y) \to (-x, -y)
\]
Applying it:
\[
(24, -15) \to (-24, 15)
\]
This does not match \( K' \).

4. **90 Degrees Counterclockwise Rotation:**
The transformation for a 90-degree counterclockwise rotation is:
\[
(x, y) \to (-y, x)
\]
Applying it:
\[
(24, -15) \to (15, 24)
\]
This does not match \( K' \).

Based on this analysis, the rotation that maps point \( K(24, -15) \) to point \( K'(-15, -24) \) is a **90 degrees clockwise rotation**.