Question

exit problems: 1. graph quadrilateral rstu with vertices r(3,1), s(5,1), t(5, - 3), and u(2,-1) and its image after a 270 degree rotation about the origin.

Explanation:

Step1: Recall rotation rule

The rule for a 270 - degree counter - clockwise rotation about the origin is $(x,y)\to(y, - x)$.

Step2: Find new coordinates of point R

For point R(3,1), using the rule $(x,y)\to(y, - x)$, we get $R'(1,-3)$.

Step3: Find new coordinates of point S

For point S(5,1), using the rule $(x,y)\to(y, - x)$, we get $S'(1,-5)$.

Step4: Find new coordinates of point T

For point T(5, - 3), using the rule $(x,y)\to(y, - x)$, we get $T'(-3,-5)$.

Step5: Find new coordinates of point U

For point U(2, - 1), using the rule $(x,y)\to(y, - x)$, we get $U'(-1,-2)$.

Answer:

The vertices of the original quadrilateral are R(3,1), S(5,1), T(5, - 3), U(2, - 1). The vertices of the rotated quadrilateral are $R'(1,-3)$, $S'(1,-5)$, $T'(-3,-5)$, $U'(-1,-2)$. To graph, plot the original points and then the rotated points on a coordinate plane.