Question

If a vertex of a triangle is (1, 1) and the mid points of two sides through the vertex are (-1, 2) and (3, 2), then the centroid of the triangle is :

• A. $1,\frac{7}{3}$
• B. $\frac{1}{3},\frac{7}{3}$
• C. $-\frac{1}{3},\frac{7}{3}$
• D. $-1,\frac{7}{3}$

Answer 1

The correct option is A $1,\frac{7}{3}$

Given $D$ is the mid point of $AB$ and $E$ is the mid point of $AC$

Let $B$ be $(a,b)$

$(\frac{a+1}{2},\frac{b+1}{2})=(-1,2)\Rightarrow a=-3,b=3$

So $B$ is $(-3,3)$

Let $C$ be $(c,d)$

$(\frac{c+1}{2},\frac{d+1}{2})=(3,2)\Rightarrow c=5,d=3$

So $C$ is $(5,3)$

Now the centroid of triangle $ABC$ is

$=(\frac{-1+1+3}{3},\frac{1+3+3}{3})=(1,\frac{7}{3})$