Line segment

Definition

A part of a straight line is called line segment.

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.

The properties of line segment are same as the properties of straight line due to the part of straight line but the only difference is, straight line has infinite length but line segment has finite measurable length.

Formation

Line segment

Geometrically, line segments are formed in two different ways but the concept of both systems is same.

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

  1. $\overleftrightarrow{ST}$ is a straight line on a plane.
  2. Cut straight line $\overleftrightarrow{ST}$ at points $U$ and $V$.
  3. The piece of straight line $\overleftrightarrow{ST}$ has end points $U$ and $V$ and it is called line segment.

The distance from point $U$ to point $V$ is equal to the length of the line segment.

formation of line segment by two joining two points

A line segment is also formed in another way geometrically on a plane.

  1. $M$ and $N$ are two points on a plane.
  2. Join the points $M$ and $N$ by a line.
  3. The line that joins points $M$ and $N$, seems as a line segment. Therefore, it is also considered as a line segment due to measurable length even it is not extracted from a straight line but imaging it as a line segment which is extracted from a straight line.

Representation

A line segment is expressed in mathematics in the form its graphical representation.

  1. Write the names of two end points of line segments but name of left point should be first and then name of right side point next.
  2. Display an overline $(―)$ symbol over the names of both two endpoints to represent the fixed length between two endpoints of the line segment.

In the first example, points $U$ and $V$ formed a line segment. The line segment which formed by points $U$ and $V$ is written as $\overline{UV}$ but its length is written as $UV$.

Similarly, the line segment which formed by points $M$ and $N$ is written as $\overline{MN}$ and its length is written as $MN$ in mathematics.

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