Question

If orthocentre and circumcentre of a triangle are respectively $(1,1)$ and $(3,2)$, then the coordinates of its centroid are:

• A. $(\frac{7}{3},\frac{5}{3})$
• B. $(\frac{5}{3},\frac{7}{3})$
• C. $(7,5)$
• D. none of these

Answer 1

The correct option is A $(\frac{7}{3},\frac{5}{3})$

We know that in a traingle the centroid divides the line joining the orthocentre and circumcentre in the ratio $2:1$,

$\therefore$ centroid is $(\frac{2\left(3\right)+1}{2+1},\frac{2\left(2\right)+1}{2+1})⟹(\frac{7}{3},\frac{5}{3})$