Question

a pentagon is transformed according to the rule ( r_{0, 180^circ} ). which is another way to state the transformation?
options (from boxes):
( (x, y) \to (x, -y) ), ( (x, y) \to (-x, y) ), ( (x, y) \to (-y, -x) ), ( (x, y) \to (-x, -y) ) (paraphrased from image)

Explanation:

Step1: Recall 180° rotation rule

A 180° rotation about the origin transforms (x,y) to (-x,-y).

Step2: Match with options

The transformation (x,y)→(-x,-y) corresponds to 180° rotation.

Answer:

(x, y) → (-x, -y)