Let the co-ordinates of $A$ and $B$ be $(x, 0)$ and $(0, y)$ $\because$ The co-ordinates of a point $P(-3,4)$ on $\{AB\}$ divides it in the ratio $2: 3$ .i.e., $\{AP\}:\{PB\}=2: 3$By using section formula, $x\;=\;\frac{m_1 x_2+m_2 x_1}{m_1+m_2}$ $-3\;=\;\frac{2 \times 0+3 \times x}{2+3}$ $\Rightarrow \;\; -3\;=\;\frac{3 x}{5} \Rightarrow 3 x=-15$ $x\;=-5$ and $y\;=\;\frac{m_1 y_2+m_2 y_1}{m_1+m_2}$ $4\;=\;\frac{2 \times y+3 \times 0}{2+3}$ $\Rightarrow\;4\;=\;\frac{2 y}{5}$ $\Rightarrow 2 y\;=20$ $\Rightarrow y\;=10$ Hence, the co-ordinates of $A$ and $B$ are ( -5 , $0)$ and $(0,10)$. .