Question

A triangle has a vertex at $(1,2)$ and the mid points of the two sides through it are $(–1,1)$ and $(2,3)$. Then the centroid of this triangle is :

• A. $(\frac{1}{3},1)$
• B. $(\frac{1}{3},2)$
• C. $(1,\frac{7}{3})$
• D. $(\frac{1}{3},\frac{5}{3})$

Answer 1

The correct option is B $(\frac{1}{3},2)$


As $E$ is the midpoint of $AB$, we get
$\frac{x_2+1}{2}=-1,\frac{y_2+2}{2}=1\Rightarrow x_2=-3,y_2=0$
Point $B$ is $(-3,0)$

Similarly, point $C$ is $(3,4)$
So, centroid of the triangle is
$(\frac{1-3+3}{3},\frac{2+0+4}{3})=(\frac{1}{3},2)$