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

Our points are A (3,-3) and B (-2, 7)

Let point C(x, 0) divide the line formed by joining by the points A and B in ratio of m:n.

By section formula,

x = , y =

For point C(x, 0)

x = , 0 =

Solving for y coordinate,

0 =

∴ 7m -3n = 0

∴ 7m = 3n

∴ =

∴ m : n = 3 : 7

Now solving for x coordinate, with m = 3 and n = 7,

x =

∴ x=

∴ x = =

Hence, the coordinates of required point is C(, 0)