Let the co-ordinates of $\mathit{A}$ and $\mathit{B}$ be $\left(\mathit{x},0\right)$ and $\left(0,\mathit{y}\right)$
$\because$ The co-ordinates of a point $\mathit{P}\left(-3,4\right)$ on $\mathrm{AB}$ divides it in the ratio $2:3$ .
i.e., $\mathrm{AP}:\mathrm{PB}=2:3$
By using section formula,
$\mathit{x}=\frac{{\mathit{m}}_1{\mathit{x}}_2+{\mathit{m}}_2{\mathit{x}}_1}{{\mathit{m}}_1+{\mathit{m}}_2}$
$-3=\frac{2\times 0+3\times \mathit{x}}{2+3}$
$\Rightarrow -3=\frac{3\mathit{x}}{5}\Rightarrow 3\mathit{x}=-15$
$\mathit{x}=-5$
and $\mathit{y}=\frac{{\mathit{m}}_1{\mathit{y}}_2+{\mathit{m}}_2{\mathit{y}}_1}{{\mathit{m}}_1+{\mathit{m}}_2}$
$4=\frac{2\times \mathit{y}+3\times 0}{2+3}$
$\Rightarrow 4=\frac{2\mathit{y}}{5}$
$\Rightarrow 2\mathit{y}=20$
$\Rightarrow \mathit{y}=10$
Hence, the co-ordinates of $\mathit{A}$ and $\mathit{B}$ are ( -5 , $0)$ and $\left(0,10\right)$. .