Question

triangle rst has vertices r(2, 0), s(4, 0), and t(1, -3). the image of triangle rst after a rotation has vertices r(0, -2), s(0, -4), and t(-3, -1). which rule describes the transformation?
r0, 90°
r0, 180°
r0, 270°
r0, 360°

Explanation:

Step1: Recall rotation rules about the origin

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

Step2: Check the transformation of point R

For point $R(2,0)$, if we apply a $270^{\circ}$ counter - clockwise rotation about the origin using the rule $(x,y)\to(y,-x)$, we get $(2,0)\to(0, - 2)$ which is $R'$.

Step3: Check the transformation of point S

For point $S(4,0)$, applying the $270^{\circ}$ counter - clockwise rotation rule $(x,y)\to(y,-x)$, we get $(4,0)\to(0,-4)$ which is $S'$.

Step4: Check the transformation of point T

For point $T(1,-3)$, applying the $270^{\circ}$ counter - clockwise rotation rule $(x,y)\to(y,-x)$, we get $(1,-3)\to(-3,-1)$ which is $T'$.

Answer:

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