Question

1. graph the figure wxyz with vertices w(-3, -2), x(-6, 1), y(-7, 0), and z(-4, -3). rotate the figure wxyz 90° clockwise and graph the rotation.
2. graph the figure wxyz with vertices w(2, -3), x(0, -1), y(-4, -5), and z(-2, -7). rotate the figure wxyz 90° counter - clockwise and graph the rotation.

Explanation:

Step1: Recall rotation rule for 90 - degree clockwise

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

Step2: Rotate point W of first figure

For $W(-3,-2)$, applying the rule: $(-3,-2)\to(-2,3)$.

Step3: Rotate point X of first figure

For $X(-6,1)$, applying the rule: $(-6,1)\to(1,6)$.

Step4: Rotate point Y of first figure

For $Y(-7,0)$, applying the rule: $(-7,0)\to(0,7)$.

Step5: Rotate point Z of first figure

For $Z(-4,-3)$, applying the rule: $(-4,-3)\to(-3,4)$.

Step6: Recall rotation rule for 90 - degree counter - clockwise

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

Step7: Rotate point W of second figure

For $W(2,-3)$, applying the rule: $(2,-3)\to(3,2)$.

Step8: Rotate point X of second figure

For $X(0,-1)$, applying the rule: $(0,-1)\to(1,0)$.

Step9: Rotate point Y of second figure

For $Y(-4,-5)$, applying the rule: $(-4,-5)\to(5,-4)$.

Step10: Rotate point Z of second figure

For $Z(-2,-7)$, applying the rule: $(-2,-7)\to(7,-2)$.

To graph the original and rotated figures, plot the original vertices on the coordinate plane first, then plot the rotated vertices and connect the points for each figure respectively.

Answer:

For the first figure $WXYZ$ with vertices $W(-3,-2),X(-6,1),Y(-7,0),Z(-4,-3)$: The 90 - degree clockwise rotated vertices are $W'(-2,3),X'(1,6),Y'(0,7),Z'(-3,4)$.
For the second figure $WXYZ$ with vertices $W(2,-3),X(0,-1),Y(-4,-5),Z(-2,-7)$: The 90 - degree counter - clockwise rotated vertices are $W'(3,2),X'(1,0),Y'(5,-4),Z'(7,-2)$.