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 the rotation rules

• For a rotation \(R_{O,\theta}\) (rotation about the origin \(O\) by an angle \(\theta\)):
• If \(\theta = 90^{\circ}\), the rule is \((x,y)\to(-y,x)\).
• If \(\theta = 180^{\circ}\), the rule is \((x,y)\to(-x, - y)\).
• If \(\theta = 270^{\circ}\), the rule is \((x,y)\to(y,-x)\).
• If \(\theta = 360^{\circ}\), a full - circle rotation about the origin. A rotation of \(360^{\circ}\) about the origin means that for any point \((x,y)\), after a \(360^{\circ}\) rotation about the origin, the point \((x,y)\) maps to itself, i.e., \((x,y)\to(x,y)\).

Answer:

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