Question

If $(3,\,\,3)$ is a vertex of a triangle and $(-3,\,\,6)$ and $(9,\,\,6)$ are the mid points of the two sides through this vertex, then the centroid of the triangle is

• A. $(3,\,\,7)$
• B. $(1,\,\,7)$
• C. $(-3,\,\,7)$
• D. $(-1,\,\,7)$

Answer 1

Answer: (A)

$(3,\,\,7)$

Answer 2

Given, $A=(3,3),E=(-3,6)$ and $F=(9,6)$ Let $B=({{x}_{1}},{{y}_{1}})$ and $C=({{x}_{2}},{{y}_{2}})$
Then, $\frac{{{x}_{1}}+3}{2}=-3,\,\,\,\,\,\,\,\,\,\,\,\,\frac{{{y}_{1}}+3}{2}=6$
$\Rightarrow$ ${{x}_{1}}=-9,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{y}_{1}}=9$
and $\frac{{{x}_{2}}+3}{2}=9,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{{{y}_{2}}+3}{2}=6$
$\Rightarrow$ ${{x}_{2}}=15,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{y}_{2}}=9$
Now, centroid $=\left( \frac{-9+15+3}{3},\frac{9+9+3}{3} \right)$
$=(3,7)$