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Q.
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
Straight Lines
Solution:
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.