Question

Prove that every line segments has one and only midpoint by drawing a figure

Answer 1

Answer:

Let us consider a line segment AB.

Assume that it has two mid-points, say C and D.

Recall that the midpoint of a line segment divides it into two equal parts and both C and D are mid-points.

That is, AC = BC  and AD = BD.

Since C is the midpoint of AB, A, C and B are collinear.

Therefore, AC + BC = AB..............(1)

Similarly, AD + DB = AB ......(2)

From (1) and (2), we get:

AC + BC = AD + DB

Or, 2AC = 2 AD

Therefore, AC = AD.

This is a contradiction, unless C and D coincide.

Therefore, our assumption that a line segment AB has two mid-points is incorrect.

Thus every line segment has one and only one midpoint.

Answer 2

Answer:

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