Let coordinates of $A$ and $B$ be $(a, 0)$ and $(0, b)$ . $\because$ The coordinate of a point $P(4,-1)$ on $AB$ divides it in the ratio $1: 2$ .i.e., $AP: PB=1: 2$By using section formula, $\;4=\;\frac{1 \times 0 + 2 \times a}{1+2}$ $\; \left[ \because x=\;\frac{m_1 x_2 + m_2 x_1}{m_1 + m_2} \right]$ $\; \Rightarrow \; \; 12=2 a \Rightarrow a=6$ $\; \text{ and } \;$ $\;-1=\;\frac{1 \times b + 2 \times 0}{1+2}$ $\; \left[ \because y=\;\frac{m_1 y_2 + m_2 y_1}{m_1 + m_2} \right]$ $\; \Rightarrow \; \; -3=b$ Hence, Coordinate of $A=(6,0)$and Coordinate of $B=(0,-3)$