Here, C is the mid-point of line segment AB, such that AC = BC.
Let us assume that there are two mid-points C and C' of same line AB.
Then as already proved, AC = 1/2 AB and also, AC' = 1/2 AB
Therefore, we get, AC = AC' ,which is only possible when C and C’ Coincide.
Hence, it is proved that every line segment has one and only one mid-point.