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

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

Step2: Check the transformation of point X

Given $X(1,3)$ and $X'(-3,1)$. If we apply the $90^{\circ}$ counter - clockwise rotation rule $(x,y)\to(-y,x)$ to $X(1,3)$, we get $(-3,1)$.

Step3: Check other points

For $Y(0,0)$, applying the $90^{\circ}$ counter - clockwise rotation rule $(0,0)\to(0,0)$. For $Z(-1,2)$, applying the $90^{\circ}$ counter - clockwise rotation rule $(-1,2)\to(-2,-1)$.

Answer:

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