Question

in a line segment AB point C is called a mid point of a line segment AB,prove that every line segment has one and only one mid point
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Answer 1

Answer:

Consider There are two midpoints of AB, C & D

So, AC=BC------(1)

AD=DB-------(2)

Substracting (1) from (2), we get,

AC-AD=CB-DB

-DC=DC (∵AC-AD=DC and CD-DB= -DC)

2DC=0

DC=0

So, distance c & D is 0, i.e C and D coincides

Thus, every line segment has one and only one mid point

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