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
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.