Question

A straight line meets the coordinate axes in $A$ and $B$. Find the equation of the straight line, when $\overline{AB}$ is divided in the ratio $1:2$ at $(-3,2)$.

Answer 1

Section formula,

$(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

$-3=\frac{2\alpha +\theta }{3}\Rightarrow \alpha =\frac{-9}{2}$

$2=\frac{\beta }{3}$

$\Rightarrow \beta =6$

By intercept form, equation of line:

$\frac{x}{\alpha }+\frac{y}{\beta }=1$

$\Rightarrow -\frac{2x}{9}+\frac{y}{6}=1$

$\Rightarrow -4x+3y=18$.