Question

point c is a midpoint of the line segment a b. prove that every line segment has one and only one midpoint

Answer 1

t us consider a line segment AB.

Assume tht it has two midpoints C and D.

so   

AC=BC and AD=BD.

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

AC+BC=AB   -(1) eq

AD+BD=AB   -(2)eq

 from (1) and (2) we get

AC+BC=AD+BD

2AC=2AD

ie AC=AD

This means C and D coincides.

Therefore every line segments have one and only one midpoint.