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In NCERT 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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Given three points A, B, and C such that C lies between A and B and AC = BC, we need to prove that AC is half of AB or AC = 1/2 AB. We can draw a figure where we mark points A, B, and C on a straight line AB and use the properties of line segments to prove that AC = 1/2 AB. Therefore, if AC = BC and C lies between A and B, then AC is half of AB.

NCERT CLASS 9 Chapter 5 INTRODUCTION TO EUCLID’S GEOMETRY
Page No. 86
Exercise 5.1
Question No. 5

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  1. Let C and D are two mid-points of line segment AB. According to question 4, we have,
    AC = 1/2 AB and AD = 1/2 AB
    ⇒ AC = AD [Things which are equal to the same thing are equal to one another]
    It is possible only if C and D coincide with each other.
    Hence, the mid-point C is unique.

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