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

• For \(R_{0,90^{\circ}}\): The rule is \((x,y)\to(-y,x)\).
• For \(R_{0,180^{\circ}}\): The rule is \((x,y)\to(-x,-y)\).
• For \(R_{0,270^{\circ}}\): The rule is \((x,y)\to(y, -x)\).
• For \(R_{0,360^{\circ}}\): Rotating a point \((x,y)\) by \(360^{\circ}\) around the origin \((0,0)\) gives \((x,y)\) since a full - circle rotation brings the point back to its original position.

Answer:

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