Question

Find the equation of the line such that its portion intercepted between the x-axis and the y-axis is divided point $(3,4)$ in the ratio $2:3$.

Answer 1

Let the equation of the line be $\frac{x}{a}+\frac{y}{b}=1$

This line meets the coordinates axes at $A(a,0)$ and $B(0,b)$ respectively. The coordinates of the point which divides the line joining $A(a,0)$ and $B(0,b)$ in the ratio $2:3$ are

$[\frac{2\times 0+3\times a}{2+3},\frac{2\times b+3\times 0}{2+3}]$

The coordinates are $(\frac{3a}{5},\frac{2b}{5})$

It is given that the point (3,4) divides AB in the ratio 2:3

$\therefore \frac{3a}{5}=3\Rightarrow a=5$

And $\frac{2a}{5}=4\Rightarrow b=10$

Hence the equation of line is

$\frac{x}{5}+\frac{y}{10}=1$

$2x+y-10=0$