Question

1. graph the figure wxyz with vertices w(-3, 5), x(-7, 9), y(-9, 7), and z(-5, 3). rotate the figure wxyz 90° clockwise and graph the rotation.
2. graph the figure wxyz with vertices w(-1, 4), x(-2, 5), y(-5, 2), and z(-4, 1). rotate the figure wxyz 90° counterclockwise and graph the rotation.

Explanation:

Step1: Recall rotation rules

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

Step2: Rotate vertices for question 5

For $W(-3,5)$ rotated 90 degrees clockwise: $( - 3,5)\to(5,3)$.
For $X(-7,9)$ rotated 90 degrees clockwise: $(-7,9)\to(9,7)$.
For $Y(-9,7)$ rotated 90 degrees clockwise: $(-9,7)\to(7,9)$.
For $Z(-5,3)$ rotated 90 degrees clockwise: $(-5,3)\to(3,5)$.

Step3: Rotate vertices for question 6

For $W(-1,4)$ rotated 90 degrees counter - clockwise: $(-1,4)\to(-4,-1)$.
For $X(-2,5)$ rotated 90 degrees counter - clockwise: $(-2,5)\to(-5,-2)$.
For $Y(-5,2)$ rotated 90 degrees counter - clockwise: $(-5,2)\to(-2,-5)$.
For $Z(-4,1)$ rotated 90 degrees counter - clockwise: $(-4,1)\to(-1,-4)$.

Answer:

For question 5, the new vertices are $W'(5,3),X'(9,7),Y'(7,9),Z'(3,5)$.
For question 6, the new vertices are $W'(-4,-1),X'(-5,-2),Y'(-2,-5),Z'(-1,-4)$.