Question

Point C is called a mid-point of line segment AB. Then every line segment has one and only one mid-point.

• A. True
• B. False

Answer 1

The correct option is A True

Let C and D be the two mid-points of line segment AB.
So, according to Euclid's axiom (4) when line is folded about point C we observe that part BC superimpose over the part AC.
It implies that
AC=BC .....(1)
Similarly D is the mid point of AB implies that AD=BD ....(2)
We have AB=AB
or AC+BC=AD+BD
or AC+AC=AD+AD [Using (1) and (2)]
or 2AC=2AD
or AC=AD .....(3)
$\text{When we superimpose AD over AC and BD over BC we find that D exactly lies over C.}$
$\text{It implies that D and C are not two different points but the same.}$
$\text{Hence we conclude that mid-point of a line segment is unique.}$