Question

1. a figure is graphed on a coordinate grid as shown. the figure is rotated 180° clockwise with the origin as the center of rotation to create a new figure. which rule describes this transformation? (x,y)→(-x,-y) ; (x,y)→(x,-y) ; (x,y)→(-y,-x) ; (x,y)→(-x,y)

Explanation:

Step1: Recall 180° rotation rule

A \(180^\circ\) clockwise (or counterclockwise) rotation about the origin has the rule: \((x, y) \to (-x, -y)\). This is because rotating a point \(180^\circ\) around the origin inverts both the \(x\)- and \(y\)-coordinates.

Step2: Analyze other options

• Option 2: \((x, y) \to (x, -y)\) is a reflection over the \(x\)-axis, not a \(180^\circ\) rotation.
• Option 3: \((x, y) \to (-y, -x)\) is a \(90^\circ\) counterclockwise rotation (or \(270^\circ\) clockwise), not \(180^\circ\).
• Option 4: \((x, y) \to (-x, y)\) is a reflection over the \(y\)-axis, not a \(180^\circ\) rotation.

Answer:

\((x, y) \to (-x, -y)\) (the first option)