Question

tanyas rotation maps point \\(k(24, -15)\\) to \\(k(-15, -24)\\). which describes the rotation?

\\(90^\circ\\) clockwise rotation
\\(270^\circ\\) clockwise rotation
\\(180^\circ\\) rotation
\\(90^\circ\\) counterclockwise rotation

Explanation:

Identify coordinates and mapping

$$ K(x, y) = K(24, -15) ightarrow K'(x', y') = K'(-15, -24) $$

Determine the transformation rule

$$ (x, y) ightarrow (y, -x) $$

Match rule to rotation description

$$ (x, y) ightarrow (y, -x) \text{ represents a } 90^\circ \text{ clockwise rotation about the origin.} $$

Answer:

• (A) 90° clockwise rotation (Correct answer)
• (B) 270° clockwise rotation
• (C) 180° rotation
• (D) 90° counterclockwise rotation