Question

Show that a line has only one midpoint

Answer 1

"HEY MATE "



HERE IS YOUR ANSWER _



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.







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