**Answer**

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 is (-4*k*+1/*k*+1, 5*k*-5/*k*+1).

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

∴ 5*k*-5/*k*+1 = 0

Therefore, *x*-axis divides it in the ratio 1:1.