Question

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

Answer 1

The coordinates of centroid $(x,y)$ of a triangle are

$x=\frac{x_1+x_2+x_3}{3}$

$y=\frac{y_1+y_2+y_3}{3}$

In the given problem,

$(x_1,y_1)=(3,-5)$

$(x_2,y_2)=(-7,4)$

$(x_3,y_3)=?$

$(x,y)=(2,-1)$

So,

$2=\frac{3-7+x_3}{3}$

$6=-4+x_3$

$x_3=6+4=10$

And

$-1=\frac{-5+4+y_3}{3}$

$-3=-1+y_3$

$y_3=-3+1=-2$