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

Answer: (E)

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, $\left(\frac{2\times 5+1\times 2}{2+1},\frac{2\times 5+1\times 2}{2+1}\right)$
$=(x,y)\Rightarrow (x,y)=(4,4)$

Hence, coordinates of centroid are $(4,4)$.