Question

a parallelogram is transformed according to the rule $(x,y)\to(x,y)$. which is another way to state the transformation? $r_{0,90^{circ}}$ $r_{0,180^{circ}}$ $r_{0,270^{circ}}$ $r_{0,360^{circ}}$

Explanation:

Step1: Analyze rotation rules

• \(R_{0,90^{\circ}}\): Rotation of \(90^{\circ}\) about the origin. The rule is \((x,y)\to(-y,x)\).
• \(R_{0,180^{\circ}}\): Rotation of \(180^{\circ}\) about the origin. The rule is \((x,y)\to(-x,-y)\).
• \(R_{0,270^{\circ}}\): Rotation of \(270^{\circ}\) about the origin. The rule is \((x,y)\to(y,-x)\).
• \(R_{0,360^{\circ}}\): Rotation of \(360^{\circ}\) about the origin. A full - circle rotation. The rule is \((x,y)\to(x,y)\) because after a \(360^{\circ}\) rotation, every point \((x,y)\) is mapped back to itself.

So the transformation \((x,y)\to(x,y)\) is equivalent to \(R_{0,360^{\circ}}\).

Answer:

\(R_{0,360^{\circ}}\)