If orthocentre and circumcentre of triangle are respectively (1, 1) and (3, 2) then the co-ordinates of its centroid are:

A) \( \Large \left(\frac{7}{3},\ \frac{5}{3}\right) \)

B) \( \Large \left(\frac{5}{3},\ \frac{7}{3}\right) \)

C) (7, 5)

D) none of these

Correct answer:
A) \( \Large \left(\frac{7}{3},\ \frac{5}{3}\right) \)

Description for Correct answer:

As we know that orthocentre, centroid and cricumcentre are collinear and centroid divides the line segment joining ortho centre and circumcentre in the ratio 2 : 1. If the points of orthocentre and circumcentre are \( \Large \left(1,\ 1\right)\ and\ \left(3,\ 2\right) \) respectively the co-ordinate of centroid is:

\( \Large \left(\frac{2.3+1.1}{2+1},\ \frac{2.2+1.1}{2+1}\right) = \left(\frac{7}{3},\ \frac{5}{3}\right) \)



Please provide the error details in above question