Question

1. graph the figure wxyz with vertices w(1, 2), x(0, 3), y(-4, -1), and z(-3, -2). rotate the figure wxyz 90° counterclockwise and graph the rotation.
2. graph the figure wxyz with vertices w(-5, -3), x(-9, 1), y(-10, 0), and z(-6, -4). rotate the figure wxyz 180° and graph the rotation.

Explanation:

Step1: Recall rotation rules

The rule for a 90 - degree counter - clockwise rotation about the origin is $(x,y)\to(-y,x)$. For a 180 - degree rotation about the origin, the rule is $(x,y)\to(-x,-y)$.

Step2: Rotate figure in question 3

For point $W(1,2)$ with 90 - degree counter - clockwise rotation: $W'( - 2,1)$. For $X(0,3)$, $X'( - 3,0)$. For $Y(-4,-1)$, $Y'(1,-4)$. For $Z(-3,-2)$, $Z'(2,-3)$.

Step3: Rotate figure in question 4

For point $W(-5,-3)$ with 180 - degree rotation: $W'(5,3)$. For $X(-9,1)$, $X'(9,-1)$. For $Y(-10,0)$, $Y'(10,0)$. For $Z(-6,-4)$, $Z'(6,4)$.

Answer:

For question 3: Rotated vertices are $W'(-2,1),X'(-3,0),Y'(1,-4),Z'(2,-3)$.
For question 4: Rotated vertices are $W'(5,3),X'(9,-1),Y'(10,0),Z'(6,4)$.