Question

In $\Delta ABC$, if the orthocenter is $(1,2)$ and the circumcenter is $(0,0)$, then centroid of $\Delta ABC$ is

• A. $(1/2,2/3)$
• B. $(1/3,2/3)$
• C. $(2/3,1)$
• D. none of these

Answer 1

The correct option is B $(1/3,2/3)$

$\begin{array}{c}If\left(x_1,y_1\right)istheorthocentre,\left(x_2,y_2\right)bethecircumcentre.\\ Centroid=\frac{2x_2+x_1}{3},\frac{2y_2+y_1}{3}\\ u\sin gtheaboveformulabytaking\left(1,2\right)as\left(x_1,y_1\right)and\left(0,0\right)as\left(x_2,y_2\right)\\ centroid=\frac{1}{3},\frac{2}{3}\end{array}$

Hence, the option $B$ is the correct answer.