Question

Prove that every line segment has only one midpoint

Answer 1

let AB be a line segment
lets assume that there r n midpoints

so n1 = 1/2 AB
n2 =1/2 AB
n3 = 1/2AB n so on.....

so....n1=n2=n3 =......so on.

Hence a line segment has only one and midpoint and its proved

Answer 2

Step-by-step explanation:

Given :-

• Let there be two midpoint C and D.
• C is the midpoint of AB.

To prove :-

Every line segment has one and only one mid-point.

Proof ....

Solution......

Let us assume ,

D be another midpoint of AB.

Therefore AD=DB ................................... Equation (1)

But it is given that C is the midpoint of AB.

Therefore AC = CB.................................. Equation (2)

Subtracting Equation (1) from Equation (2) , we get ...

AC - AD = CB - DB

DC = - DC

2DC =0

DC = 0

Therefore C and D coincides.

Thus , every line segment has one and only one midpoint.

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