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 the transformation rule

The rule $(x,y)\to(x,y)$ means no - change.

Step2: Recall rotation rules

A rotation of $R_{0,\theta}$ about the origin:

• $R_{0,90^{\circ}}$: $(x,y)\to(-y,x)$
• $R_{0,180^{\circ}}$: $(x,y)\to(-x,-y)$
• $R_{0,270^{\circ}}$: $(x,y)\to(y, - x)$
• $R_{0,360^{\circ}}$: A full - rotation brings a point back to its original position, i.e., $(x,y)\to(x,y)$. So the transformation $(x,y)\to(x,y)$ is equivalent to $R_{0,360^{\circ}}$.

Answer:

D. $R_{0,360^{\circ}}$