Question

Find the ratio in which the line segment joining the points $A(1,-5)$ and $B(-4,5)$ is divided by the $X$-axis. Also find the coordinates of the point of division.

Answer 1

Let ratio be $k:1$

Hence

$m_1=k,m_2=1$

Given

point $A$, $x_1=1,y_1=-5$

point $B$, $x_2=-4,y_2=5$

Given P lies on X-axis, then it's Y-coordinate must be zero.

$x=x,y=0$

Using section formula

$y=\frac{m_1{y}_2+m_2{y}_1}{m_1+m_2}$

$0=\frac{k\times 5+1\times (-5)}{k+1}$

$0=\frac{5k-5}{k+1}$

$5k-5=0$

$5k=5$

$k=1$

Hence, $k=1$

Now,

$x=\frac{m_1{x}_2+m_2{x}_1}{m_1+m_2}$

$x=\frac{k\times (-4)+1\times 1}{k+1}$

$x=\frac{1\times (-4)+1\times 1}{1+1}$

$x=\frac{-3}{2}$

Hence the coordinate of point $P(x,0)=P(\frac{-3}{2},0)$