If a triangle has its orthocentre at (1, 1) and circumcentre at $\left(\frac{3}{2},\frac{3}{4}\right)$ then the coordinates of the centroid of
the triangle are

Since the centroid divides the line joining the orthocentre and circumcentre in the ratio 2 : 1 internally, therefore, if the centroid is (x, y), then

$x=\frac{2.{\displaystyle \frac{3}{2}}+1.1}{2+1}=\frac{4}{3} and y=\frac{2.{\displaystyle \frac{3}{4}}+1.1}{2+1}=\frac{5}{6}$

$\therefore$ Coordinates of centroid are $\left(\frac{4}{3},\frac{5}{6}\right)$