Question

e. triangle npq with coordinates n(12, - 3), p(1, 2), and q(9, 0) is rotated 180° about the origin.

Explanation:

Step1: Recall rotation rule

When a point $(x,y)$ is rotated 180° about the origin, the new - point is $(-x,-y)$.

Step2: Find new coordinates of N

For point N(12, - 3), after 180° rotation about the origin, the new coordinates are $N'(-12,3)$ since $x = 12,y=-3$ and the new $x=-12$, new $y = 3$.

Step3: Find new coordinates of P

For point P(1,2), after 180° rotation about the origin, the new coordinates are $P'(-1,-2)$ since $x = 1,y = 2$ and the new $x=-1$, new $y=-2$.

Step4: Find new coordinates of Q

For point Q(9,0), after 180° rotation about the origin, the new coordinates are $Q'(-9,0)$ since $x = 9,y = 0$ and the new $x=-9$, new $y = 0$.

Answer:

The coordinates of the rotated triangle are $N'(-12,3),P'(-1,-2),Q'(-9,0)$