Question
Point C is called a mid point of line segment AB, prove that every line segment has one and only one mid-point.
✓
Answer
Let a line AB have two mid-points, say, C and D. Then
AB = AC + CB = 2AC . . . . (i) . . . [As C is the mid-point of AB]
and AB = AD + DB = 2AD . . . . (ii) [As D is the mid-point of AB]
From equation (i) and (ii)
AC = AD and CB = DB
But this will possible only when D lies on point C. So every line segment has one and only one mid-point.
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