To determine the type of rotation that maps point [tex]\( K(24, -15) \)[/tex] to [tex]\( K'(-15, -24) \)[/tex], we need to analyze how the coordinates change under various rotations.
1. 90 degrees clockwise rotation:
- This transforms a point [tex]\( (x, y) \)[/tex] to [tex]\( (y, -x) \)[/tex].
- Applying this to [tex]\( K(24, -15) \)[/tex]: [tex]\( (24, -15) \)[/tex] becomes [tex]\( (-15, -24) \)[/tex].
2. 270 degrees clockwise rotation:
- This is equivalent to a 90 degrees counterclockwise rotation, transforming [tex]\( (x, y) \)[/tex] to [tex]\( (-y, x) \)[/tex].
- Applying this to [tex]\( K(24, -15) \)[/tex]: [tex]\( (24, -15) \)[/tex] becomes [tex]\( (15, 24) \)[/tex].
3. 180 degrees rotation:
- This transforms a point [tex]\( (x, y) \)[/tex] to [tex]\( (-x, -y) \)[/tex].
- Applying this to [tex]\( K(24, -15) \)[/tex]: [tex]\( (24, -15) \)[/tex] becomes [tex]\( (-24, 15) \)[/tex].
4. 90 degrees counterclockwise rotation:
- This transforms a point [tex]\( (x, y) \)[/tex] to [tex]\( (-y, x) \)[/tex].
- Applying this to [tex]\( K(24, -15) \)[/tex]: [tex]\( (24, -15) \)[/tex] becomes [tex]\( (15, 24) \)[/tex].
On examining the transformations, we see that the coordinates transform [tex]\( K(24, -15) \)[/tex] to [tex]\( K'(-15, -24) \)[/tex] correctly through a 90 degrees clockwise rotation. Thus, the correct description of the rotation that maps [tex]\( K \)[/tex] to [tex]\( K' \)[/tex] is:
90 degrees clockwise rotation.
