Question

1. polygon pqrs has vertices p(-3,1), q(-4,3), r(0,3), and s(-1,1). graph the figure and its image after a counterclockwise rotation of 180° about the origin. then write the coordinates of polygon pqrs.

Explanation:

Step1: Recall rotation rule

The rule for a 180 - degree counter - clockwise rotation about the origin is $(x,y)\to(-x,-y)$.

Step2: Apply rule to point P

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

Step3: Apply rule to point Q

For point $Q(-4,3)$, using the rule $(x,y)\to(-x,-y)$, we get $Q'=(4,-3)$.

Step4: Apply rule to point R

For point $R(0,3)$, using the rule $(x,y)\to(-x,-y)$, we get $R'=(0,-3)$.

Step5: Apply rule to point S

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

Answer:

$P'(3, - 1),Q'(4,-3),R'(0,-3),S'(1,-1)$