Question

Find the third vartex of a $△ABC$ if two of its vertices are $B\left(-3,1\right)$ and $C\left(0,-2\right)$ and its centroid is at the origin.

Answer 1

Centriod coordinates are given by $(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

As it is at origin $\Rightarrow x_1+x_2+x_3=0$

$\Rightarrow x_3=3$ also $y_1+y_2+y_3=0$ $y_3=-1+2=1$

$\Rightarrow (x_3,y_3)=(3,1)$