Given point [tex]\( K(8, -6) \)[/tex], we need to determine which rotation maps it to [tex]\( K'(-6, -8) \)[/tex].
Let's consider the possible rotations:
1. 90° clockwise rotation:
- A 90° clockwise rotation of a point [tex]\( (x, y) \)[/tex] results in [tex]\( (y, -x) \)[/tex].
- Applying this to point [tex]\( (8, -6) \)[/tex]:
[tex]\[ K'(8, -6) \rightarrow (-6, -8) \][/tex]
2. 90° counterclockwise rotation:
- A 90° counterclockwise rotation of a point [tex]\( (x, y) \)[/tex] results in [tex]\( (-y, x) \)[/tex].
- Applying this to point [tex]\( (8, -6) \)[/tex]:
[tex]\[ K'(8, -6) \rightarrow (6, 8) \][/tex]
3. 180° rotation (clockwise or counterclockwise):
- A 180° rotation of a point [tex]\( (x, y) \)[/tex] results in [tex]\( (-x, -y) \)[/tex].
- Applying this to point [tex]\( (8, -6) \)[/tex]:
[tex]\[ K'(8, -6) \rightarrow (-8, 6) \][/tex]
From the above calculations, only the 90° clockwise rotation maps the original point [tex]\( K(8, -6) \)[/tex] to the final point [tex]\( K'(-6, -8) \)[/tex].
Therefore, the correct rotation is:
[tex]\[ \boxed{90^{\circ} \text{ clockwise rotation}} \][/tex]
