Question

geometry practice g.co.a.5 rotations www.jmap.org

1. graph the figure wxyz with vertices w(-2, -1), x(-4, 1), y(-7, -2), and z(-5, -4). rotate the figure wxyz 180° and graph the rotation.
2. graph the figure wxyz with vertices w(4, 4), x(1, 7), y(-1, 5), and z(2, 2). rotate the figure wxyz 90° clockwise and graph the rotation.

Explanation:

Step1: Recall rotation rules

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

Step2: Solve for 180 - degree rotation of first figure

Given $W(-2,-1)$, after 180 - degree rotation, $W'=(2,1)$.
Given $X(-4,1)$, after 180 - degree rotation, $X'=(4,-1)$.
Given $Y(-7,-2)$, after 180 - degree rotation, $Y'=(7,2)$.
Given $Z(-5,-4)$, after 180 - degree rotation, $Z'=(5,4)$.

Step3: Solve for 90 - degree clockwise rotation of second figure

Given $W(4,4)$, after 90 - degree clockwise rotation, $W'(4,-4)$.
Given $X(1,7)$, after 90 - degree clockwise rotation, $X'(7,-1)$.
Given $Y(-1,5)$, after 90 - degree clockwise rotation, $Y'(5,1)$.
Given $Z(2,2)$, after 90 - degree clockwise rotation, $Z'(2,-2)$.

Answer:

For the first figure with 180 - degree rotation: New vertices are $W'(2,1),X'(4,-1),Y'(7,2),Z'(5,4)$.
For the second figure with 90 - degree clockwise rotation: New vertices are $W'(4,-4),X'(7,-1),Y'(5,1),Z'(2,-2)$.