Question

Equations to the sides of a triangle are $x-3y=0$, $4x+3y=5$ and $3x+y=0$. The line $3x-4y=0$ passes through the

• A. incentre
• B. circumcentre
• C. centroid
• D. orthocentre of the triangle

Answer 1

The correct option is D

orthocentre of the triangle

Sides $x-3y=0$ and $3x+y=0$ of the triangle are perpendicular to each other. Hence, the triangle is right angled at origin, which is the point of intersection of these sides. This implies that the origin is the orthocentre of the triangle and the line $3x-4y=0$ passes which passes through the origin, passes through the orthocentre of the triangle.