Question

1. a figure was transformed on a coordinate grid using the rule (x, y) → (-x, -y). which of the following describes this transformation? a reflection across the x-axis a reflection across the y-axis a 90° clockwise rotation about the origin a 180° clockwise rotation about the origin

Explanation:

Step1: Recall transformation rules

• Reflection over x - axis: \((x,y)\to(x, - y)\)
• Reflection over y - axis: \((x,y)\to(-x,y)\)
• \(90^{\circ}\) clockwise rotation about origin: \((x,y)\to(y, - x)\)
• \(180^{\circ}\) clockwise rotation about origin: \((x,y)\to(-x, - y)\)

Step2: Match the given rule

The given transformation rule is \((x,y)\to(-x, - y)\), which matches the rule for a \(180^{\circ}\) clockwise rotation about the origin.

Answer:

D. A \(180^{\circ}\) clockwise rotation about the origin