Find the ratio in which the segment joining the points (1, -3) and (4, 5) is divided by the x-axis.

Let the points be A(1, -3) and B(4, 5). Let the x-axis divide the line segment AB in the ratio k:1.
The coordinates of the point dividing the line segment joining (x1, y1) and (x2, y2) in the ratio m:n are given by:
$\left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\right)$
In this case, (x1, y1) = (1, -3) and (x2, y2) = (4, 5), and the ratio is k:1.
The coordinates of the point dividing AB in the ratio k:1 are:
$\left(\frac{4k + 1}{k+1}, \frac{5k - 3}{k+1}\right)$
Since the point lies on the x-axis, its y-coordinate is 0.
$\frac{5k - 3}{k+1} = 0$
$5k - 3 = 0$
$5k = 3$
$k = \frac{3}{5}$
Therefore, the ratio in which the x-axis divides the line segment joining the points (1, -3) and (4, 5) is 3:5.