Question

Find the equation to the straight line which passes through the point (-4, 3) and is such that the portion of it between the axes is divided by the point in the ratio 5:3.Trace the straight line whose equation are ?

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 5:3 are

$[\frac{5\left(0\right)+3\ast a}{5+3},\frac{5\left(b\right)+3\times 0}{5+3}]$

(i.e) The coordinates are $[\frac{3a}{8},\frac{5b}{8}]$

It is given that the point (-4, 3) divides AB in the ratio 5 : 3

$\frac{3a}{8}=-4$

$a=\frac{-33}{3}$

$\frac{5b}{8}=3$

$b=\frac{24}{5}$

Hence the equation of the line is

$\frac{x}{\frac{-33}{3}}+\frac{y}{\frac{24}{5}}=1$

$9x-20y=-96$

$9x-20y+96=0$