Let the ratio in which the line segment joining A (1, – 5) and B (– 4, 5) is divided by x-axis be k : 1.

Therefore, the coordinates of the point of division, say P(x, y) is 

or P(x, y) = \(\frac{-4k+1}{k+1}, \frac{5k-5}{k+1}\)

We know that y-coordinate of any point on x-axis is 0.

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

5k = 5

or k = 1

So, x-axis divides the line segment in the ratio 1:1.

Now, find the coordinates of the point of division:

P (x, y) = \(\frac{-4\times 1+1}{1+1}, \frac{5\times 1 -5}{1+1}\)

= \( (\frac{-3}{2}, 0)\)