Question

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

Explanation:

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

Answer:

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