Q. 265.0( 3 Votes )
The question consists of two statements, namely, Assertion (A) and Reason (R), Please select the correct answer.
A. Both Assertion (A) and (R) are true and Reason (R) is a correct explanation of Assertion (A).
B. Both Assertion (A) and Reason (R) are true but Reason (R) is a correct explanation of Assertion (A).
C. Assertion (A) is true and Reason (R) is false.
D. Assertion (A) is false and Reason (R) is true.
Answer :
Let us consider, a line segment AB.
Assume that it has two midpoints say C and D
Recall that the midpoint of a line segment divides it into two equal parts
That is AC = BC and AD = DB
Since C is midpoint of AB, we have A, C and B are collinear
∴ AC + BC = AB → (1)
Similarly, we get AD + DB = AB → (2)
From (1) and (2), we get
AC + BC = AD + DB
2 AC = 2AD
∴ AC = AD
This is a contradiction unless C and D coincide.
Therefore our assumption that a line segment AB has two midpoints is incorrect.
Thus every line segment has one and only one midpoint.
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