Question

what transformation is represented by the rule $(x, y)\to(-x, -y)$?
reflection across the x - axis
reflection across the y - axis
rotation of $90^{circ}$ counterclockwise about the origin
rotation of $180^{circ}$ about the origin

Explanation:

Step1: Recall reflection and rotation rules

• Reflection across \(x\) - axis: \((x,y)\to(x, - y)\)
• Reflection across \(y\) - axis: \((x,y)\to(-x,y)\)
• Rotation of \(90^{\circ}\) counter - clockwise about the origin: \((x,y)\to(-y,x)\)
• Rotation of \(180^{\circ}\) about the origin: \((x,y)\to(-x,-y)\)

Answer:

rotation of \(180^{\circ}\) about the origin