Question

Prove that : a line segment has only 1 mid point

Answer 1

Let a line segment has 2 mid points.

Answer 2

i can feel a nice proof by contradiction emerging here.
assume there are 2 mid points :P

Answer 3

or better, assume that more then one mid point exists.

Answer 4

Then AC = BC as C is the mid point............................... (1)

Also, AD = BD as D is the mid point -----------------(2)

2AC = AB
and
2AD =AB
Thus,

AC = AD
Also, C and D lie on the same line
Thus, C and D should coincide

Thus, we have reached a contradiction

Thus, a line segment has a only 1 mid point