In $\Delta ABC$ , orthocentre and circumcentre are at $\left(2,3\right)$ and $\left(5,-6\right)$ respectively. Then the centroid is

Given orthocentre $O=\left(2,3\right)$

Circumcentre $S=\left(5,-6\right)$

We know that,

Orthocentre, centroid divides circumcentre in the ratio $2:1$

Point divides internally

$P\left(x,y\right)=\left[\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n}\right]$

$=\left[\frac{2\left(5\right)+1\left(2\right)}{3},\frac{2\left(-6\right)+\left(3\right)}{3}\right]$

$=\left[\frac{12}{3},-\frac{9}{3}\right]$

$=\left[4,-3\right]$