Question

for exercises 10 and 11, polygon qrst has vertices q(-5, -1), r(-3, 1), s(-2, -2), and t(-4, -5). write the coordinate notation for each rotation given. then write the coordinates of polygon qrst after each rotation. 10. counterclockwise rotation of 270° about the origin 11. clockwise rotation of 180° about the origin

Explanation:

Step1: Recall rotation rules

For a counter - clockwise rotation of 270° about the origin, the coordinate transformation rule is $(x,y)\to(y, - x)$. For a clock - wise rotation of 180° about the origin, the rule is $(x,y)\to(-x,-y)$.

Step2: Rotate point Q for 270° counter - clockwise

Given $Q(-5,-1)$, using the rule $(x,y)\to(y, - x)$, we get $Q'(-1,5)$.

Step3: Rotate point R for 270° counter - clockwise

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

Step4: Rotate point S for 270° counter - clockwise

Given $S(-2,-2)$, using the rule $(x,y)\to(y, - x)$, we get $S'(-2,2)$.

Step5: Rotate point T for 270° counter - clockwise

Given $T(-4,-5)$, using the rule $(x,y)\to(y, - x)$, we get $T'(-5,4)$.

Step6: Rotate point Q for 180° clock - wise

Given $Q(-5,-1)$, using the rule $(x,y)\to(-x,-y)$, we get $Q'(5,1)$.

Step7: Rotate point R for 180° clock - wise

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

Step8: Rotate point S for 180° clock - wise

Given $S(-2,-2)$, using the rule $(x,y)\to(-x,-y)$, we get $S'(2,2)$.

Step9: Rotate point T for 180° clock - wise

Given $T(-4,-5)$, using the rule $(x,y)\to(-x,-y)$, we get $T'(4,5)$.

Answer:

For 10: Coordinate notation: $(x,y)\to(y, - x)$. Vertices of $Q'R'S'T'$ are $Q'(-1,5)$, $R'(1,3)$, $S'(-2,2)$, $T'(-5,4)$.
For 11: Coordinate notation: $(x,y)\to(-x,-y)$. Vertices of $Q'R'S'T'$ are $Q'(5,1)$, $R'(3,-1)$, $S'(2,2)$, $T'(4,5)$.