Question

ACAD. Lapram vy urawing uc ugure.
In Ouestion 4. point C is called a mid-point of line segment AB. Prove that every line
segment has one and only one mid-point.​

Answer 1

SOLUTION

It is given that,

C is the mid point of line segment AB.

such that AC= BC.

Let there are two mid points C & C' of AB

=) AC= 1/2AB

& AC'= AC'

Which is only possible when C & C' coincide.

Point C' lies on C

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

hope it helps ☺️⬆️

Answer 2

Step-by-step explanation:

Let us consider, a line segment AB. Assume that it has two midpoints say C and D �Recall that the midpoint of a line segment divides it into two equal parts That is AC = BC and AD = DB Since C is midpoint of AB, we have A, C and B are collinear ∴ AC + BC = AB → (1) Similarly, we get AD + DB = AB → (2) From (1) and (2), we get AC + BC = AD + DB 2 AC = 2AD ∴ AC = AD This is a contradiction unless C and D coincide. Therefore our assumption that a line segment AB has two midpoints is incorrect. Thus every line segment has one and only one midpoint.