Question

type the correct answer in this box.
rectangle pqrs is rotated 180° clockwise about the origin to create rectangle pqrs. complete the rule that describes the coordinates of rectangle pqrs after the rotation has occurred.

$(x, y) = (-x, -y)$

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 - and y - coordinates across the origin, negating their values.

Step2: Apply to rectangle's coordinates

For any vertex \((x,y)\) of rectangle PQRS, after a 180° clockwise rotation about the origin, the new coordinates \((x',y')\) of the corresponding vertex in rectangle \(P'Q'R'S'\) follow the rule \((x',y') = (-x,-y)\).

Answer:

\((x', y') = (-x, -y)\)