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Let us consider a point C that lies between two points A and B such that AC = BC then point C is called a midpoint of line segment AB.

What is the number of midpoints a line segment AB has?

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Two mid-point

One and only one midpoint

Infinitely many mid-point

Four mid-point

answer is B.

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Detailed Solution

It is given that point C lies between two points A and B such that AC = BC and C is the mid-point of the line segment AB.
Question Image

Therefore, we have,

A C = 12 A B (1)

Assume that point D is also the midpoint of line segment AB. Question Image

Then we have,

A D = 12 A B (2)

By subtracting equation (1) from equation (2), we get,

A D − A C = 12 A B − 12 A B

⇒ A D − A C = 0

⇒ A D = A C

⇒ C D = 0

This shows that the distance between points C and D is zero.
Therefore, points C and D coincide.
Hence, line segment AB has one and only one midpoint.
Thus, option (2) is correct.

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