Question

If coordinates of the circumcentre and the orthocentre of a triangle are respectively $(5,5)$ and $(2,2)$, then the coordinates of the centroid are

• A. $(1,1)$
• B. $(3,1)$
• C. $(3,3)$
• D. $(2,2)$
• E. $(4,4)$

Answer 1

The correct option is E $(4,4)$

The circumcentre $O$, centroid $G$ and orthocentre $O^{{}^{\prime }}$ of a triangle are collinear.
$G$ divides $O^{{}^{\prime }}O$ in the ratio $2:1$.
Let the coordinates of $G$ be $(x,y)$.
Then, $(\frac{2\times 5+1\times 2}{2+1},\frac{2\times 5+1\times 2}{2+1})$
$=(x,y)\Rightarrow (x,y)=(4,4)$
Hence, coordinates of centroid are $(4,4)$.