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Q.

Choose whether the statement is true or false: If point C is the midpoint of line segment AB. Prove that every line segment has one and only one midpoint.

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a

True

b

False

answer is A.

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Detailed Solution

Let's assume C to be the mid-point of AB
Thus, AC = BC
Adding AC on both sides, we get
Or, AC + AC = BC + AC (BC + AC coincides to AB)
Or, 2 AC = AB
Or, AC =

\frac{1}{2 AB}

-----(1)
Let us consider a point D lying on AB,
Let's assume that D is another mid-point of AB.
Therefore AD = BD
Adding equal length AD on both sides, we get
AD + AD = BD + AD (BD + AD coincides to AB)
Or, 2 AD = AB
Or, AD =

\frac{1}{2 AB}

------(2)
From equations (1) and (2), we can conclude that AC = AD
Hence the given statement is true.

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