Question

julios rotation maps point ( k(-6,9) ) to ( k(9,6) ). which describes the rotation?
( 90^{circ} ) counterclockwise rotation
( 90^{circ} ) clockwise rotation
( 270^{circ} ) clockwise rotation
( 180^{circ} ) rotation

Explanation:

Step1: Recall rotation rules

• For a \(90^{\circ}\) counter - clockwise rotation about the origin, the rule is \((x,y)\to(-y,x)\).
• For a \(90^{\circ}\) clockwise rotation about the origin, the rule is \((x,y)\to(y, - x)\).
• For a \(270^{\circ}\) clockwise rotation about the origin, the rule is \((x,y)\to(-y,x)\) (since \(270^{\circ}\) clockwise is equivalent to \(90^{\circ}\) counter - clockwise).
• For a \(180^{\circ}\) rotation about the origin, the rule is \((x,y)\to(-x,-y)\).

Step2: Apply the rules to the point \(K(-6,9)\)

• For \(90^{\circ}\) counter - clockwise rotation: \((-6,9)\to(-9,-6)\).
• For \(90^{\circ}\) clockwise rotation: \((-6,9)\to(9,6)\).
• For \(270^{\circ}\) clockwise rotation: \((-6,9)\to(-9,-6)\).
• For \(180^{\circ}\) rotation: \((-6,9)\to(6,-9)\).

Answer:

\(90^{\circ}\) clockwise rotation