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? r0,180° r0,270° r0,90° r0,360°

Explanation:

Step1: Recall rotation rules about the origin

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

For point $X(1,3)$, if we apply a $90^{\circ}$ counter - clockwise rotation about the origin using the rule $(x,y)\to(-y,x)$, we get $(-3,1)$ which is $X'$.

Step3: Check the transformation of point Y

For point $Y(0,0)$, for any rotation about the origin, $(0,0)$ remains $(0,0)$. Here $Y(0,0)$ and $Y'(0,0)$.

Step4: Check the transformation of point Z

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

Answer:

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