Find the ratio in which the line segment joining the points A(3, −3) and B(−2, 7) is divided by x-axis.

The line segment joining the points A(3, − 3) and B(− 2, 7) is divided by x-axis. Let the required ratio be k : 1. So,

$0=\frac{k(7)-3}{k+1} \Rightarrow k=\frac{3}{7}$

Now

Point of division $=\left(\frac{k(-2)+3}{k+1}, \frac{k(7)-3}{k+1}\right)$

$=\left(\frac{\frac{3}{7} \times(-2)+3}{\frac{3}{7}+1}, \frac{\frac{3}{7} \times(7)-3}{\frac{3}{7}+1}\right) \quad\left(\because k=\frac{3}{7}\right)$

$=\left(\frac{-6+21}{3+7}, \frac{21-21}{3+7}\right)$

$=\left(\frac{3}{2}, 0\right)$

Hence, the required ratio is $3: 7$ and the point of division is $\left(\frac{3}{2}, 0\right)$.