Question

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

Answer 1

C is the mid-point of AB

Now, there be two mid points of AB i.e C and D.

AC = BD .......(i)

AD = CB .......(ii)

Subtracting (i) from (ii) ,

AC - AD = BD - CB

-DC = DC

2DC = 0

DC = 0

So, distance between C and D = 0 i.e C and D coincides.

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

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Diagram in attachment :)