In Question 4, point C is called a mid-point of the segment AB. Prove that every line segment has one and only one mid-point.
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In Question 4, point C is called a mid-point of the segment AB. Prove that every line segment has one and only one mid-point.
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C is the mid-point of AB
Now, there be two mid points of AB i.e C and D.
AC = BD .......(i)
AD = CB .......(ii)
Subtracting (i) from (ii) ,
AC - AD = BD - CB
-DC = DC
2DC = 0
DC = 0
So, distance between C and D = 0 i.e C and D coincides.
Thus, every line segment has one and only one mid point.
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Diagram in attachment :)