Question

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

Explanation:

Step1: Recall rotation rules

The rule for a $90^{\circ}$ counter - clockwise rotation about the origin $(0,0)$ is $(x,y)\to(-y,x)$. The rule for a $180^{\circ}$ rotation about the origin is $(x,y)\to(-x,-y)$. The rule for a $270^{\circ}$ counter - clockwise rotation about the origin is $(x,y)\to(y, - x)$. The rule for a $360^{\circ}$ rotation about the origin is $(x,y)\to(x,y)$.

Step2: Match the given rule

The given transformation rule is $(x,y)\to(y,-x)$, which matches the rule for a $270^{\circ}$ counter - clockwise rotation about the origin, denoted as $R_{0,270^{\circ}}$.

Answer:

C. $R_{0,270^{\circ}}$