Question

If a line intercepted between the coordinate axes is trisected at a point $A(4,3)$, which is nearer to $x$-axis, then its equation is :

• A. $4x—3y=7$
• B. $3x+2y=18$
• C. $3x+8y=36$
• D. $x+3y=13$

Answer 1

Answer: (B)

$\Rightarrow 4=\left(\frac{1\times 0+2\times a}{1+2}\right)=\frac{2a}{3}$
$\Rightarrow a=6\Rightarrow$ coordinate of $B$ is $B\left(6,0\right)$
$3=\left(\frac{1\times a+2\times 0}{1+2}\right)=\frac{b}{3}$
$\Rightarrow b=9$ and $C\left(0,9\right)$
Slope of line passing through $\left(6,0\right),\left(0,9\right)$
slope, $m=\frac{9}{-6}=-\frac{3}{2}$
Equation of line $y-0=\frac{-3}{2}\left(x-6\right)$
$2y=-3x+18$
$3x+2y=18$