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2014-09-12T21:21:53+05:30
A line segment is a part of aline which has definite length which has two end points so the midpoint will be half of definite length and it is only one.

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2014-09-12T21:23:19+05:30
Let us consider a line segment AB.
Assume tht it has two midpoints C and D.


so   
AC=BC and AD=BD.
Since C is the midpoint A,C and B are collinear.
AC+BC=AB   -(1) eq
AD+BD=AB   -(2)eq
 from (1) and (2) we get
AC+BC=AD+BD
2AC=2AD
ie AC=AD

This means C and D coincides.
Therefore every line segments have one and only one midpoint.
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