Question

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

Answer 1

Given ,

The line segment joining A(1, -5) and B(-4, 5) is divided by the x axis

Let , the x axis divides the given line segment in the ratio m : n

We know that , the section formula is given by

$\boxed{ \sf{x = \frac{ mx_{2} + nx_{1}}{m + n} \: , \: y = \frac{ my_{2} + ny_{1}}{m + n} }}$

Thus ,

$\implies \tt 0 = \frac{ 5m - 5n}{m + n}$

$\implies \tt 0 = 5m - 5n$

$\implies \tt 5n = 5m$

$\implies \tt \frac{m}{n} = \frac{5}{5}$

$\implies \tt m : n = 1 : 1$

★ The ratio in which x axis divides the given line segment is 1 : 1

Now , the coordinate of the point of division will be

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

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

★ The point (-3/2 , 0) divides the given line segment