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In Question 4, point C is called a mi...

In Question 4, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.

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Let the given line AB has two mid-points C and D.
`therefore" "AC=CB" "(because" C is the mid-point of AB")`….(1)
and `AD = DB" "(because" D is the mid-point of AB")`….(2)
Subtracting eq. (2) from eq. (1), we get
`AC-AD=CB-DB`
`rArr" "-(AD-AC)=CB-DB`
`rArr" "-CD=CD`
`or" "CD-CD=CD+CD` (if equals added to equals then wholes are equal)
`rArr" "0=2CD`
`rArr" "CD=0`
`therefore` C and D coincide.
Thus, every line segment has one and only mid-point. Hence Proved.
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