Question

Two vertices of a triangle are $(3,-5)$ and $(-7,4)$, If its centroid is $(2,1)$, find the third vertex.

Answer 1

centroid $=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

$(x_1,y_1)=(3,-5);x_2,y_2=(-7,4)$

$(2,1)=[\frac{3-7+x_3}{3},\frac{-5+4+y_3}{3}]$

$x_3-4=3\left(2\right);y_3-1=3\left(1\right)$

$x_3=10;y_3=4$

$(10,4)$ is third point