Question

The equation of two sides of a triangle are $3x+4y-12=0,2x+y-8=0.$ If the circumcentre is $\left(0 , 3\right),$ then the centroid of the triangle is

• A. $\left(0 , \frac{7}{3}\right)$
• B. $\left(0 , \frac{14}{3}\right)$
• C. $\left(0 , \frac{16}{3}\right)$
• D. $\left(0 , 6\right)$

Answer 1

Answer: (B)

Foot of perpendicular from $\left(0 , 3\right)$ on the line
$2x+y-8=0$ is $\left(2 , 4\right)$
Hence, $P$ is $\left(0 , 8\right)$ which is orthocentre
$\therefore $ Centroid is $\left(0 , \frac{14}{3}\right)$