Question

quadrilateral klmn is rotated 180° counterclockwise about the origin to produce quadrilateral klmn. write the rule for the rotation. (x, y) → (\boxed{ }, \boxed{ })

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(180^{\circ}\) counter - clockwise about the origin, the rule is \((x,y)\to(-x,-y)\).

Step2: Verify with a point

Take point \(K\) with coordinates \((- 2,8)\). After rotation, \(K'\) has coordinates \((2,-8)\). Using the rule \((x = - 2,y = 8)\), \(-x=-(-2)=2\) and \(-y=-8\).

Answer:

\((x,y)\to(-x,-y)\)