Question

A straight line through the point $A(3,4)$ is such that its intercept between the axes is bisected at $A$. Its equation is

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

Answer 1

The correct option is C $4x+3y=24$

Let the equation ofthe line be $\frac{x}{a}+\frac{y}{b}=1$ which meets the x and y axis at $P(a,0)$ and $Q(0,b)$ respectively.

The coordinate of midpoint of PQ are $(\frac{a}{2},\frac{b}{2})$ Since $A(3,4)$ bisects PQ $\Rightarrow \frac{a}{2}=3,\frac{b}{2}=4$

$\Rightarrow a=6,b=8$ $\therefore$ required line is

$\frac{x}{6}+\frac{y}{8}=1\Rightarrow 4x+3y=24$