To determine the specific rotation that maps point [tex]\( K(24, -15) \)[/tex] to [tex]\( K'( -15, -24) \)[/tex], let’s carefully analyze the given points and identify the transformation step-by-step.
1. Identify Initial Coordinates:
[tex]\( K = (24, -15) \)[/tex].
2. Identify Final Coordinates:
[tex]\( K' = (-15, -24) \)[/tex].
3. Understanding the Rotation:
- A rotation transformation involves rotating the points around the origin [tex]\((0, 0)\)[/tex].
- When we talk about rotations, we use angles measured in degrees with specified directions:
- Clockwise Rotation: Rotating to the right.
- Counterclockwise Rotation: Rotating to the left.
4. Analyze Coordinate Changes:
- To determine how the coordinates changed, consider the typical rotations:
- 90[tex]\(^\circ\)[/tex] Clockwise: [tex]$(x, y)$[/tex] turns into [tex]$(y, -x)$[/tex].
- 180[tex]\(^\circ\)[/tex] Rotation: [tex]$(x, y)$[/tex] turns into [tex]$(-x, -y)$[/tex].
- 90[tex]\(^\circ\)[/tex] Counterclockwise: [tex]$(x, y)$[/tex] turns into [tex]$(-y, x)$[/tex].
- 270[tex]\(^\circ\)[/tex] Clockwise (equals 90[tex]\(^\circ\)[/tex] Counterclockwise): [tex]$(x, y)$[/tex] turns into [tex]$(-y, x)$[/tex].
5. Applying Transformations on Original Point [tex]\(K\)[/tex]:
- Initial point [tex]\(K(24, -15)\)[/tex]:
- 90[tex]\(^\circ\)[/tex] Clockwise Rotation:
- [tex]$(x, y) \rightarrow (y, -x)$[/tex]
- [tex]$(24, -15) \rightarrow (-15, -24)$[/tex]
6. Result Comparison:
- By applying the 90[tex]\(^\circ\)[/tex] clockwise rotation to the point [tex]\(K(24, -15)\)[/tex], the result indeed matches the coordinates of [tex]\(K'(-15, -24)\)[/tex].
Given this analysis, the correct description of the rotation that maps point [tex]\(K(24, -15)\)[/tex] to [tex]\(K'(-15, -24)\)[/tex] is:
[tex]\[ \boxed{90^\circ \text{ clockwise rotation}} \][/tex]
