Question

If orthocenter and circumcenter of a triangle are respectively $(1,1)$ and $(3,2)$ then the co ordinates of its centroid are

• A. $(\frac{7}{3},\frac{5}{3})$
• B. $(\frac{5}{3},\frac{7}{3})$
• C. $(7,5)$
• D. None of these

Answer 1

The correct option is A $(\frac{7}{3},\frac{5}{3})$

Given, orthocenter$=H=(1,1)$

Circumcenter$=0=(3,2)$

We know that, $H\mu :{\mu }_0=2:1$

$\therefore \mu =\frac{20+H}{3}$

$=(\frac{2\times 3+1}{3},\frac{2\times 2+1}{3})$

$\therefore$Centroid$=\mu =(\frac{7}{3},\frac{5}{3})$