Question

$\huge\mathbb{\underline{Question}}$

Prove that there is one and only midpoint P to the line segment XY .​

Answer 1

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.

I hope it is useful! !!!!

Thanku

Answer 2

Answer:

Let AB be a line segment 

and let D and E be its two midpoints 

now, since D is the midpoints of AB 

so, AD=DB

AB=AD+DB=2AD (1)

Also E is a point of AB

So, AE=EB

AB=AE+EB=2AE (2)

From eq 1 &2

2AD=2AE

D and E coincide to each other

AB has one and only one mid points

Hence every line segments has one and only one midpoint.

Hope its helpful