Question

If a straight line passing through the point $P(-3,4)$ is such that its intercepted portion between the coordinate axes is bisected at $P$, the its equation is :

• A. $4x+3y=0$
• B. $x-y+7=0$
• C. $3x-4y+25=0$
• D. $4x-3y+24=0$

Answer 1

The correct option is D $4x-3y+24=0$

Let the line cuts $x$-axis and $y$-axis at $A(h,0)$ and $B(0,k)$ respectively.
$\therefore$ Coordinates of mid-point of $AB$ is $P$
$P(-3,4)\equiv (\frac{h}{2},\frac{k}{2})$
$\therefore h=-6$ and $k=8$

Therefore, equation of line is
$\frac{x}{-6}+\frac{y}{8}=1$
$\Rightarrow 4x-3y+24=0$