Question

quadrilateral abcd is transformed according to the rule (x, y) → (y, -x). which is another way to state the transformation?
r₀,₉₀°
r₀,₁₈₀°
r₀,₂₇₀°
r₀,₃₆₀°

Explanation:

Step1: Recall rotation rules

A rotation of a point $(x,y)$ counter - clockwise about the origin $(0,0)$ by an angle $\theta$ has the following general transformation rules. For a $90^{\circ}$ counter - clockwise rotation $R_{0,90^{\circ}}$, the rule is $(x,y)\to(-y,x)$. For a $180^{\circ}$ counter - clockwise rotation $R_{0,180^{\circ}}$, the rule is $(x,y)\to(-x,-y)$. For a $270^{\circ}$ counter - clockwise rotation $R_{0,270^{\circ}}$, the rule is $(x,y)\to(y, - x)$. For a $360^{\circ}$ counter - clockwise rotation $R_{0,360^{\circ}}$, the rule 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.

Answer:

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