Question

if then form examlpe a segment has exactly one midpoint

Answer 1

Let us consider a line segment AB
Assume that it has two mid points say C and D

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 A                 C               D                    B

Recall that the mid point of a line segment divides it into two equal parts.
 So, AC = BC and AD = BD
Since, C is the midpoint of AB So we have A , C and B are collinear
∴ AC + BC = AB
Similarly AD + BD = AB
From both equations, we get:
AC + BC = AD +BD
2 AC = 2 AD
AC = AD
This is a contradiction unless C and D coincide.
Therefore our assumption that a line segment has two different points is incorrect.
Thus every line segment has only one midpoint.