Let coordinates of $\mathrm{A}$ and $\mathrm{B}$ be $\left(\mathit{a},0\right)$ and $\left(0,\mathit{b}\right)$ .
$\because$ The coordinate of a point $\mathrm{P}\left(4,-1\right)$ on $\mathrm{AB}$ divides it in the ratio $1:2$ .
i.e., $\mathrm{AP}:\mathrm{PB}=1:2$
By using section formula,
$4=\frac{1\times 0+2\times \mathit{a}}{1+2}$
$\left[\because \mathit{x}=\frac{{\mathit{m}}_1{\mathit{x}}_2+{\mathit{m}}_2{\mathit{x}}_1}{{\mathit{m}}_1+{\mathit{m}}_2}\right]$
$\Rightarrow 12=2\mathit{a}\Rightarrow \mathit{a}=6$
$-1=\frac{1\times \mathit{b}+2\times 0}{1+2}$
$\left[\because \mathit{y}=\frac{{\mathit{m}}_1{\mathit{y}}_2+{\mathit{m}}_2{\mathit{y}}_1}{{\mathit{m}}_1+{\mathit{m}}_2}\right]$
$\Rightarrow -3=\mathit{b}$
Hence, Coordinate of $\mathrm{A}=\left(6,0\right)$
and Coordinate of $\mathit{B}=\left(0,-3\right)$