The Concept

Distance between two points  P(x1, y1z1)  and Q(x2, y2z2) is given by


Section Formula

The co-ordinates of the point R which divides the join of  A(x1, y1z1)  and B(x2, y2z2)in the ratio m:n are:

When m = n, we find the co-ordinates of the mid-point of PQ as:

The co-ordinates of any points on the line joining two points

P(x1, y1z1)  and P(x2, y2z2)   are:

Where  k  ≠ −1

If k takes only positive real values, we get the co-ordinates of the points on the Segment PQ (except P and Q).