Question

hexagon defghi is rotated 180° clockwise about the origin to produce hexagon defghi. write the rule for the rotation. (x, y) → (□, □)

Explanation:

Step1: Recall 180° rotation rule

A 180° clockwise (or counterclockwise) rotation about the origin transforms a point \((x, y)\) to \((-x, -y)\). This is because rotating 180° flips both the x - coordinate and y - coordinate across the origin.

Step2: Apply the rule to the hexagon's vertices

For any vertex \((x, y)\) of hexagon \(DEFGHI\), after a 180° clockwise rotation about the origin, its image \(D'E'F'G'H'I'\) will have the vertex \((-x, -y)\). So the rule for the rotation is \((x, y)\to(-x, -y)\).

Answer:

\((-x, -y)\)