The question consists of two statements, namely, Assertion (A) and Reason (R), Please select the correct answer. Assertion (A) Reason (R) Every line segment has a unique mid-point. A point C is called the mid-point of a line segment A/B, if C is an interior point of AB and AC=CB.

Question

Philoid · Accepted 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.

Assertion (A)	Reason (R)
Every line segment has a unique mid-point.	A point C is called the mid-point of a line segment A/B, if C is an interior point of AB and AC=CB.

The question consists of two statements, namely, Assertion (A) and Reason (R), Please select the correct answer.Assertion (A)Reason (R)Every line segment has a unique mid-point.A point C is called the mid-point of a line segment A/B, if C is an interior point of AB and AC=CB.

The question consists of two statements, namely, Assertion (A) and Reason (R), Please select the correct answer.

Assertion (A)

Reason (R)

Every line segment has a unique mid-point.

A point C is called the mid-point of a line segment A/B, if C is an interior point of AB and AC=CB.