Question

If the circumcentre of the triangle lies at $(0,0)$ and centroid is the mid point of the line joining the points $(2,3)$ and $(4,7)$, then its orthocentre lies on the line

• A. $5x-3y=0$
• B. $5x-3y+6=0$
• C. $5x+3y=0$
• D. $5x+3y+6=0$

Answer 1

Answer: (A)

$5x-3y=0$

Circumcentre $\equiv (0,0)$

Centroid $=$ Mid point of $(2,3)$ & $(4,7)$

Centroid $\equiv (\frac{2+4}{2},\frac{7+3}{2})=(3,5)$

For any $\Delta$, centroid, circumcentre and orthocentre all lie in one line

$\therefore$ The equation of line passing through $(0,0)$ and $(3,5)$ is

$y-0=\frac{5-0}{3-0}(x-0)$

$\Rightarrow 3y=5x$

$\Rightarrow 5x-3y=0$

Hence, option A.