To determine the type of rotation that maps point [tex]\( K(17, -12) \)[/tex] to point [tex]\( K(12, 17) \)[/tex], let's analyze the coordinate transformations associated with different rotations:
1. 90 degrees counterclockwise rotation:
The transformation rule for a 90-degree counterclockwise rotation is [tex]\((x, y) \rightarrow (-y, x)\)[/tex].
Applying this rule to point [tex]\( (17, -12) \)[/tex]:
[tex]\[
(17, -12) \rightarrow (-(-12), 17) = (12, 17)
\][/tex]
This transformation matches the resulting point [tex]\( (12, 17) \)[/tex].
2. 270 degrees counterclockwise rotation (which is equivalent to 90 degrees clockwise):
The transformation rule for a 270-degree counterclockwise (or 90-degree clockwise) rotation is [tex]\((x, y) \rightarrow (y, -x)\)[/tex].
Applying this rule to point [tex]\( (17, -12) \)[/tex]:
[tex]\[
(17, -12) \rightarrow (-12, -17)
\][/tex]
This does not match the resulting point [tex]\( (12, 17) \)[/tex].
3. 180 degrees rotation:
The transformation rule for a 180-degree rotation is [tex]\((x, y) \rightarrow (-x, -y)\)[/tex].
Applying this rule to point [tex]\( (17, -12) \)[/tex]:
[tex]\[
(17, -12) \rightarrow (-17, 12)
\][/tex]
This does not match the resulting point [tex]\( (12, 17) \)[/tex].
From these analyses, it is clear that the transformation of [tex]\( K(17, -12) \)[/tex] to [tex]\( K(12, 17) \)[/tex] can be described by a [tex]\( 90^\circ \)[/tex] counterclockwise rotation.
Therefore, the correct description of the rotation is:
[tex]\[ \boxed{90^{\circ} \text{ counterclockwise rotation}} \][/tex]
