Theorem: (Mid–point formula)
The mid-point M(x, y) of the line segment with end points A(x₁, y₁) and B(x₂, y₂) has coordinates.

Proof:
Let D be midpoint of  Then D has coordinate  and Let S be midpoint of  Then S has coordinate 

But hence D and M have the same abscissa  and hence M and S have the same ordinate,