Question

triangle xyz has vertices x(1, 3), y(0, 0), and z(-1, 2). the image of triangle xyz after a rotation has vertices x(-3, 1), y(0, 0), and z(-2, -1). which rule describes the transformation?
$r_{0,90^{circ}}$
$r_{0,180^{circ}}$
$r_{0,270^{circ}}$
$r_{0,360^{circ}}$

Explanation:

Step1: Recall rotation rules

For a $90^{\circ}$ counter - clockwise rotation about the origin $(x,y)\to(-y,x)$.
For point $X(1,3)$: applying the rule $(x,y)\to(-y,x)$ gives $(-3,1)$ which is $X'$.

Step2: Check other points

For point $Y(0,0)$, applying $(x,y)\to(-y,x)$ gives $(0,0)$ which is $Y'$.
For point $Z(-1,2)$, applying $(x,y)\to(-y,x)$ gives $(-2, - 1)$ which is $Z'$.
So the rotation is a $90^{\circ}$ counter - clockwise rotation about the origin, described by $R_{0,90^{\circ}}$.

Answer:

A. $R_{0,90^{\circ}}$