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State whether the statement is true or false.

Every line segment has a unique midpoint.

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False

True

answer is A.

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Detailed Solution

Using the following concepts,
• Every line segment contains a single midpoint.
• A midpoint is a point on a line segment that divides it into two equal halves.
Suppose

P

and

Q

are the midpoints of line segment A and B.
If

P = Q

then, the midpoints of the line segment are unique.
As we know,

Q

is a midpoint,
Therefore,

Q

divides AB into equal halves,
=

A Q = Q B

…….(1)
And when

P

is a midpoint,

P

divides AB into equal halves,
=

A P = P B

……..(2)
Subtracting (2) from (1),

A P − A Q = P B − Q B P Q = − P Q 2 P Q = 0 P Q = 0

This implies that

P = Q

, thus

P

and

Q

coincide.
Therefore, every midpoint of a line segment is unique.
Hence, option 1 is correct, and the given statement is true.

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