Line segment

A part of a straight line is called a line segment.

Actually, the meaning of line segment is derived from two words “Line” and “Segment”.

1. The meaning of Line is a straight path.
2. The meaning of segment is a part.

A line segment is graphically represented by a line with two endpoints. It is also known as a line between two points.

Representation

1. Graphically, a line segment is represented by a line with two endpoints.
2. A line segment is written in mathematics on the basis of graphical representation. So, write names of points one after one and display a line over both points.

Formation

A line segment is formed geometrically in two different ways.

Part of Straight Line

A line segment is basically an extracted part from a straight line.

$\overleftrightarrow{EF}$ is a straight line in a plane and identify any two points ($P$ and $Q$) on the line. Then, extract the small line at points $P$ and $Q$ from the straight line.

The small line which contains $P$ and $Q$ as endpoints, is a part of the straight line $\overleftrightarrow{EF}$. Therefore, it is called as a line segment geometrically.

On the basis of graphical representation of a line segment, the line segment in this example is written as $\overline{PQ}$ and its length is written as $PQ$ in mathematics.

Line between Points

A line that joins any two points in a plane is considered as a line segment. There are two main reasons for this consideration.

1. The small line contains two endpoints.
2. The distance between two endpoints can be measured and it is equal to the length of the small line.

$M$ and $N$ are two points in a plane and join them by a line. The distance between the two points is equal to the length of the line. Moreover, it seems a line segment. Therefore, a line that joins any two points in a plane can be considered as a line segment.

The line segment is written as $\overline{MN}$ in mathematics and its length is represented by $MN$.