Question

a parallelogram is transformed according to the rule (x,y)→(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 properties

A rotation \(R_{O,\theta}\) about the origin \(O\). A rotation of \(360^{\circ}\) about the origin maps any point \((x,y)\) to \((x,y)\) itself.

Step2: Check other rotation angles

• A rotation \(R_{O,90^{\circ}}\) maps \((x,y)\) to \((-y,x)\).
• A rotation \(R_{O,180^{\circ}}\) maps \((x,y)\) to \((-x,-y)\).
• A rotation \(R_{O,270^{\circ}}\) maps \((x,y)\) to \((y, -x)\).

Answer:

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