Question

Find the ratio in which the line segment joining the points A(3, −3) and B(−2, 7) is divided by x-axis.
Also, find the point of division. [CBSE 2015]

Answer 1

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,
$0=\frac{k\left(7\right)-3}{k+1}\Rightarrow k=\frac{3}{7}$
Now
$$\begin{gathered} \mathrm{Point}\mathrm{of}\mathrm{division}=\left(\frac{k\left(-2\right)+3}{k+1},\frac{k\left(7\right)-3}{k+1}\right) \\ =\left(\frac{{\displaystyle \frac{3}{7}}\times \left(-2\right)+3}{{\displaystyle \frac{3}{7}}+1},\frac{{\displaystyle \frac{3}{7}}\times \left(7\right)-3}{{\displaystyle \frac{3}{7}}+1}\right)\left(\because k=\frac{3}{7}\right) \\ =\left(\frac{{\displaystyle -6+21}}{{\displaystyle 3+7}},\frac{{\displaystyle 21-21}}{{\displaystyle 3+7}}\right) \\ =\left(\frac{{\displaystyle 3}}{{\displaystyle 2}},0\right) \end{gathered}$$
Hence, the required ratio is 3 : 7 and the point of division is $\left(\frac{3}{2},0\right)$.