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

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

Answer 1

Answer: (C)

Given equation of line are,
$l_1:x-3y=0$,Slope $m_1=\frac{1}{3}$
$l_2:4x+3y=5$ slope $m_2=-\frac{4}{3}$
$l_3:3x+y=0$ slope $m_3=-3$
Here $m_1\times m_3=-1$ Line $l_1\perp l_3$
Slope of given line: $3x-4y=0,m=\frac{3}{4}$
herem $\times m_2=-1$
$\therefore$ Given line is perpendicular to ${\text{Linel}}_2$
Therefore The given line must pass throigh the orthocenter