Question

The equation of 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. centroid
• C. orthocentre
• D. circumcentre

Answer 1

Answer: (C)

Sides of the triangle are $x-3y=0$,
$4x+3y=5$ and
$3x+y=0$
By seeing the equation of the sides we can easily find out that $x-3y=0$ and $3x+y=0$ are perpendicular to each other.
So, they will cut each other at orthocentre.
Solving $x-3y=0$ and $3x+y=0$,
we find $x=0$,
$y=0$.
When we put $x=0$,
$y=0$ in $3x-4y=0$,
we find $0=0$ (satisfied).
So, line $3x-4y=0$ passes through orthocentre.