Question

△ghi is rotated 180° counterclockwise about the origin to produce △g′h′i′. write the rule for the rotation. (x, y) → (□, □)

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 \(G(5, - 2)\). After rotation, \(G'\) should be \((-5,2)\) which matches the graph. Take point \(H(-3,-7)\). After rotation, \(H'\) should be \((3,7)\) which matches the graph. Take point \(I(5,2)\). After rotation, \(I'\) should be \((-5,-2)\) which matches the graph.

Answer:

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