Question

1. triangle xyz with vertices x(4, -1), y(8, -2), and z(1, -8): 180° about the origin x(_, _) y(_, _) z(_, _)

Explanation:

Step1: Recall rotation rule

The rule for rotating a point $(x,y)$ 180° about the origin is $(x,y)\to(-x,-y)$.

Step2: Find $X'$

For point $X(4, - 1)$, applying the rule: $X(4,-1)\to X'(-4,1)$.

Step3: Find $Y'$

For point $Y(8,-2)$, applying the rule: $Y(8,-2)\to Y'(-8,2)$.

Step4: Find $Z'$

For point $Z(1,-8)$, applying the rule: $Z(1,-8)\to Z'(-1,8)$.

Answer:

$X'(-4,1)$
$Y'(-8,2)$
$Z'(-1,8)$