Question

if then form of a segment has exactly one midpoint

Answer 1

let us we have a segment of line EF

                    E                                                                  F

So here we can say we have two mid-point k and also J.

               E                            k                 J                  F

Remembered the mid-point segment of the line. First we will have divided segment of a line into two equal parts.

So here,

EK = JK or EJ = FJ

Since, k is the midpoint of the line segment EF that we have E, k and j are the collinear.

         Ek + JK = EF

Similarly, we can say

EJ + FK = EF

From the both of the equations, we can get.

EK + JK = EJ +FK

2EK = 2 EJ

EK = EJ

As we know it is a contradiction unless K & J coincide.

So that is why our assumption at the segment of the line have two different points is incorrect.

Now we can say that is why every segment of the line have a one midpoint