Find the ratio in which the line segment joining the points $\displaystyle \mathrm{A}(6,3)$ and B$\displaystyle (-2, -5)$ is divided by $\displaystyle x$-axis.

Let \(\displaystyle \mathrm{P}(\mathrm{x}, 0)\) be the point on x axis which divides AB in the ratio k : $\displaystyle 1$ \[\frac{-5 \mathrm{k}+3}{k+1}=0 \Rightarrow \mathrm{k}=\frac{3}{5} \] Ratio is $\displaystyle 3$ : $\displaystyle 5$