Question

Find t he third vertex of a triangle if two of its vertices are at (-2,4) and (7,-1) are centroid at (3,2).

Answer 1

We have,

Let the point

$A(x_1,y_1)=(-2,4)$

$B(x_2,y_2)=(7,-1)$

$C(x_3,y_3)=?$

And centroid $(x,y)=(3,2)$

Now, we know that,

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

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

$(3,2)=(\frac{5+x_3}{3},\frac{3+y_3}{3})$

$3=\frac{5+x_3}{3},2=\frac{3+y_3}{3}$

$x_3=9-5=4$

$y_3=6-3=3$

$\text{Now,}$

$(x_3,y_3)=(4,3)$

Hence, this is the answer.