Question

1. the vertices of △xyz are x(-4, 7), y(0, 8), and z(2, -1).

a. what are the vertices of r_(180°, o) (△xyz)?
z(4,-7), y(0,-8) z(0,-8) z(-2,-1)
check answer
b. what are the vertices of r_(270°, o) (△xyz)?

Explanation:

Step1: Recall 180 - degree rotation rule

The rule for a 180 - degree rotation about the origin $(0,0)$ is $(x,y)\to(-x,-y)$.

Step2: Apply rule to point X

For $X(-4,7)$, $(-4,7)\to(4, - 7)$.

Step3: Apply rule to point Y

For $Y(0,8)$, $(0,8)\to(0,-8)$.

Step4: Apply rule to point Z

For $Z(2,-1)$, $(2,-1)\to(-2,1)$.

for part b:

Step1: Recall 270 - degree rotation rule

The rule for a 270 - degree rotation about the origin $(0,0)$ is $(x,y)\to(y,-x)$.

Step2: Apply rule to point X

For $X(-4,7)$, $(-4,7)\to(7,4)$.

Step3: Apply rule to point Y

For $Y(0,8)$, $(0,8)\to(8,0)$.

Step4: Apply rule to point Z

For $Z(2,-1)$, $(2,-1)\to(-1,-2)$.

Answer:

The vertices of $r_{(180^{\circ},O)}(\triangle XYZ)$ are $X'(4,-7)$, $Y'(0,-8)$, $Z'(-2,1)$.