Question

If two of the vertices of triangle are $A(3,4,4)$ and $B(-4,5,-3)$ and the centroid of the triangle is at $G(-1,2,1)$, then find the coordinates of the third vertex C of the triangle.

Answer 1

Let vertex $C(x,y,z)$

$(-1,2,1)=(\frac{3-4+x}{3},\frac{4+5+y}{3},\frac{4-3+z}{3})$

$⟹x=-2,y=-3,z=2$