Find the ratio in which the line segment joining the points A(3, -3) and B(-2, 7) is divided by the x-axis. Also find the coordinates of the point of division.

Given line segment joining points A(3, -3) and B(-2, 7)
Let the coordinate of the point be P(x, 0) and the required ratio be k:1
Assume m = k, n = 1
Using section formula:
(mx2 + nx1 / m + n, my2 + ny1 / m + n)
Substitute the values, we get P(x, 0) = (k(-2) + 3k + 1, k(7) + 1(-3) / k + 1) ⇒ P(x, 0) = (-2k + 3 / k + 1, 7k -3 / k + 1)
Comparing both sides:
x = -2k + 3 / k + 1 ——— (1)
0 = 7k - 3 / k + 1 ——— (2)
From equation (2), 7k - 3 = 0 ⇒ 7k = 3 ⇒ k = 3/7
Plug the value of k in equation 1,
x = -2(3/7) + 3 / 3/7 + 1 ⇒ x = 1.5
Therefore, Ratio (k:1) = 3:7
Thus x-axis divides the line in the ratio 3:7
Coordinate point of division P(x, 0) = (1.5, 0)