Question

1. rectangle tuvw with vertices t(-3, -1), u(0, -2), v(-2, -8), and w(-5, -7): 90° counterclockwise
2. triangle ghi with vertices g(0, -2), h(7, -6), and i(3, -8): 270° counterclockwise
3. rectangle wxyz with vertices w(-3, -5)

Explanation:

Step1: Recall rotation rule

The rule for a 90 - degree counter - clockwise rotation about the origin is $(x,y)\to(-y,x)$.

Step2: Rotate point T

For $T(-3,-1)$, using the rule $(-3,-1)\to(1, - 3)$.

Step3: Rotate point U

For $U(0,-2)$, using the rule $(0,-2)\to(2,0)$.

Step4: Rotate point V

For $V(-2,-8)$, using the rule $(-2,-8)\to(8,-2)$.

Step5: Rotate point W

For $W(-5,-7)$, using the rule $(-5,-7)\to(7,-5)$.

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

Step6: Rotate point G

For $G(0,-2)$, using the rule $(0,-2)\to(-2,0)$.

Step7: Rotate point H

For $H(7,-6)$, using the rule $(7,-6)\to(-6,-7)$.

Step8: Rotate point I

For $I(3,-8)$, using the rule $(3,-8)\to(-8,-3)$.

Answer:

For rectangle $TUVW$: $T'(1, - 3)$, $U'(2,0)$, $V'(8,-2)$, $W'(7,-5)$
For triangle $GHI$: $G'(-2,0)$, $H'(-6,-7)$, $I'(-8,-3)$