• # question_answer 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)  $(-1,\,\,7)$

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 $=\left( \frac{-9+15+3}{3},\frac{9+9+3}{3} \right)$ $=(3,7)$