Line Segment - Definition, Formula, Examples - Cuemath

Line Segment

A line segment is a part of a line that has two endpoints and a fixed length. It is different from a line that can be extended in both directions and which does not have a beginning or an end. In this lesson, let us learn more about the line segment definition, the line segment symbol, and how to find the length of a line segment.

1.	What is a Line Segment?
2.	How to Measure Line Segments?
3.	Line Segment Formula
4.	Difference Between Line, Line Segment, and Ray
5.	FAQs on Line Segment

What is a Line Segment?

A line segment is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon. The figure given below shows a line segment AB, where the length of line segment AB refers to the distance between its endpoints, A and B.

Line Segment Definition

A line segment can be defined as a part of a line which a fixed length that can be measured.

Line Segment Symbol

A line segment is represented by a bar on top which is the line segment symbol. It is written as \(\overline{AB}\).

How to Measure Line Segments?

Line segments can be measured with the help of a ruler (scale). Let us see how to measure a given line segment and name it PQ.

• Step 1: Place the tip of the ruler carefully so that zero is placed at the starting point P of the given line segment.
• Step 2: Now, start reading the values given on the ruler and spot the number which comes on the other endpoint Q.
• Step 3: Thus, the length of the line segment is 4 inches, which can be written as \(\overline{PQ}\) = 4 inches.

Line Segment Formula

In the above example, we measured the length of line segment PQ to be 4 inches. This is written as \(\overline{PQ}\) = 4 inches. Now, let us see how to find the length of a line segment when the coordinates of the two endpoints are given. In this case, we use the distance formula, that is, D = √[(\(x_{2}-x_{1}\))2 + (\(y_{2}-y_{1}\))2]. Here, (\(x_{1}\), \(y_{1}\)) and (\(x_{2}\), \(y_{2}\)) are the coordinates of the given points.

For example, a line segment has the following coordinates: (-2, 1) and (4, –3). Let us apply the distance formula to find the length of the line segment. Here, \(x_{1}\) = -2; \(x_{2}\) = 4; \(y_{1}\) = 1; \(y_{2}\) = -3. After substituting these values in the distance formula we get: D =√[(4-(-2))2 + (-3-1)2) = √((4+2)2 + (-3-1)2] = √(62 + (-4)2) = √(36 + 16) = √52 = 7.21 units. Therefore, using the distance formula, we found that the length of the line segment with coordinates (-2, 1) and (4, –3) is 7.21 units.

Difference Between Line, Line Segment, and Ray

Observe the figures given below to understand the difference between a line, a line segment, and a ray.

Line	Line Segment	Ray
A line is a set of points that extends in two opposite directions indefinitely.	A line segment is a part of a line and has a beginning point and an endpoint.	A ray is a part of a line that has a start point but no definite endpoint.
It is indicated with arrows at both ends to show that it continues forever.	It has a definite length and is indicated with two endpoints.	It shows one start point and an arrow at the other end which means that it goes on forever in one direction.
It has no endpoints and is written as \(\overleftrightarrow{AB}\).	It is denoted by a bar on top which is the line segment symbol. It is written as \(\overline{CD}\).	It is written as \( \overrightarrow{\mathrm{EF}}\).

Important Notes

• A line has indefinite ends and cannot be measured.
• A line segment has a start point and an endpoint, thus, it can be measured.
• Line segments have a defined length, hence, they form the sides of any polygon.
• A ray has just one start point and no endpoint, therefore, it cannot be measured.
• The concept of rays can be understood with the example of the rays of the sun, which have a beginning point but no endpoint.

☛Related Topics

Check out the following pages related to the line segment.

• Difference Between Line and Line Segment
• Lines, Rays and Line Segments Worksheets
• How do you know if two line segments are perpendicular?