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# In question 4, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.

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 = $$\frac{1}{2}$$ AB and also, AC' = $$\frac{1}{2}$$ 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.