Section formula:
The coordinates of point which divides line segment joining 2 given points A(x1, y1) and B(x2, y2) internally in the ratio given m : n are
The coordinates of the point P(x, y) which divides A (x1, y1) and B (x2, y2) externally in ratio m:n are
Illustration: Find the ratio in which x-axis and y-axis divides the line segment joining (-2, - 3) and (-1, 2).
Key concept: If ratio, in which a given line segment can be divided, is to be determined, then for convenience instead of taking m:n, we take ratio k:1. If the value of k turns out to be positive, it is the internal division and if k is negative it is an external division.
Solution: Let x-axis divides line segment in k : 1. Then coordinate of point on x-axis which divides PQ in K : 1 is
. But if any point is lying on x-axis, then its y-coordinate will be zero
Hence x - axis divides PQ in 3:2 internally. Likewise coordinates of any point on y-axis which divides PQ in k :1 is 
. But if any point is lying on y-axis, then it is x-coordinate will always zero
Thus y-axis divides PQ in 2:1 externally
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