Line Segment: Definition, Measurement, Formulas, Examples

A Line Segment is a fixed-length segment of a line in geometry. The line segment is the line drawn between two fixed points.  Thus, a line segment can have a fixed length. In this article, let’s learn everything about the Line segments in detail.

Any point on the line can be connected by a line segment. Although the line has no endpoints and can expand indefinitely in both directions, the line segment between two points has a set length. Continue reading to know more.

Definition of Line Segment

In mathematics, line segment, line are the basic concepts for constructing geometrical shapes. In geometry, the line segment is the part of the line with a fixed distance. We can say that the line segment has a finite length, whereas the line does not have any fixed length.

According to Euclid’s concept, the line is the breadthless length.

1. A line is the basic geometric figure, which connects all points on it.
2. A line has no endpoints, and it extends infinitely in both directions.
3. A line segment is the part of the line.
4. The line segment connects any two points on the line.

The part or portion of the line between points \(A\) and \(B\) is called the line segment in the figure below. Thus, \(AB\) is the line segment.

The line segment is the connected way of the two points, which we can measure. Also, line segments are used to form the sides of the polygon.

Symbol of Line Segment

A line segment is the part of the line that connects any two points on the line.

Here, line segment \(AB\) is the distance between endpoints \(A\) and \(B.\) The line segment joining the two endpoints, \(A\) and \(B,\) is denoted by the bar symbol \(\left( – \right)\) such as \(\overline {AB} .\)

Measuring a Line Segment

Line segments are measured by using different methods:

Observation

It is a general method to compare the two line segments. Just by observing any two line segments, we can say which one is larger and shorter in length. This type of method is not suggestible because it won’t give exact measurements sometimes.

In the above figure, by observing, we can say that line segment \(AB\) is larger, and line segment \(CD\) is smaller.

Trace Paper

Two line segments can be easily compared using trace paper. Trace any one of the line segments and place it on the other. We may easily compare two line segments by visualising these. Repeat the process if you want to compare more than two line segments. For a proper comparison, the line segments must be traced accurately.

Ruler

As seen in the diagram below, a ruler has certain markings that begin at zero. All of the markings on the ruler are equal sections, each measuring one centimetre in length. Each part is subdivided into ten equal pieces once again, with each sub-part measuring one.

Steps to be followed measuring the line segment by using the ruler as follows:

1. Adjust the tip of the ruler carefully such that starting point or one end of the line segment placed on the zero marking of the ruler.
2. Now, measure and count the markings on the scales starting from zero to the other end of the line segment.

In the above figure, the length of the line segment \(AB\) is \(8\,{\text{cm}},\) as there are eight equal markings on the ruler.

Construction of Line Segment

The line drawn between two fixed points is called the line segment. A line segment can have a fixed length. The different methods for drawing the line segments are

1. Construction of a Line Segment using a Ruler
2. Construction of a Line Segment using Ruler and Compasses

Construction of a Line Segment Using Ruler

Constructing a line segment using a ruler is the easiest and the simplest method of drawing a line segment. The steps to be followed are discussed below:

1. Consider a ruler (scale), place it on the paper.
2. Mark the zero marking point of the ruler as a starting point, say \(A.\)
3. Take the required length (say \(6\,{\text{cm}}\)) on the ruler and mark the endpoint as \(B.\)
4. Thus, the portion AB gives the required line segment of length \(6\,{\text{cm}}{\text{.}}\)

Construction of a Line Segment Using Ruler and Compass

One of the ways of constructing a line segment using the ruler and compass. The steps to be followed are given below:

1. First, draw a line of any length.
2. Mark a point on the line as \(A\) (say), which is the starting point of the line segment.
3. Take a compass and place the tip of the compass on the zero marking of the ruler.
4. Adjust the pencil to the required length (say \(6\,{\text{cm}}\)) on the ruler.

5. Placing the tip of the compass at starting point \(A\) of the line and mark arc on the line.

6. Mark the point as \(B.\)
7. Thus, the portion of line \(AB\) (say \(6\,{\text{cm}}\)) is known as a line segment.

Line Segment Formula

We know that the line segment has two endpoints. The length of the line segment when the coordinates of two endpoints are given can be calculated by using the distance formula.

We know that the distance between two points, say \(P\) and \(Q,\) with coordinates \(\left( {{x_1},{y_1}} \right)\) and \(\left( {{x_2},{y_2}} \right)\) is given by
\(PQ = \sqrt {{{\left({{x_2} – {x_1}} \right)}^2} + {{\left({{y_2} – {y_1}} \right)}^2}} \)

The above-given distance formula is known as the line segment formula.

Differences Between Line and Line Segment

Line segment connects any points on the line. The line has no endpoints, it can extend infinitely in both directions, but the line segment has a fixed length in between two points.

Line	Line segment
A line is a breadthless length	A line segment is a part of the line with a fixed-length
The line has no endpoints with infinite length	The line segment has two endpoints with a fixed-length
The line can be represented by placing the arrow marks on both sides. Example:\(\overleftrightarrow {AB}\)	A line segment can be represented by placing the bar over the letters. Example: \(\overline {CD} \)

Difference Between Line Segment and Ray

Ray	Line segment
A ray is the part of the line, which starts from one point and extends in one direction.	The line segment has two endpoints with a fixed-length
Ray can be represented by placing the arrow marks on one side. Example: \(\overrightarrow {EF} \)	A line segment can be represented by placing the bar over the letters. Example: \(\overline {CD} \)

Solved Examples

Q.1. How many line segments are there in the given triangle, and name all the line segments.

Ans: We know that the line segment is the connected part or portion of the line in between two points. The line segment has two endpoints with a fixed point. The line segments are used to construct polygons.

In the given triangle, we have three line segments. The line segments are denoted by placing the bar over the points. The lines segments in the given triangle \(ABC\) are \(\overline {AB} ,\overline {BC} \) and \(\overline {CA} .\)

Q.2. Construct a line segment of length \(6\,{\text{cm}}\) by using a ruler and compass.
Ans: The steps to be followed to construct a line segment of length \(6\,{\text{cm}}\) is given below:
1. First, draw a line of any length.
2. Mark a point on the line as \(A\) (say), which is the starting point of the line segment.
3. Take a compass and place the tip of the compass on the zero marking of the ruler.
4. Adjust the pencil to the required length of \(6\,{\text{cm}}\) on the ruler.

5. Placing the tip of the compass at starting point \(A\) of the line and mark arc on the line.

6. Mark the point as \(B.\)
7. Thus, the portion of line \(AB\) is known as a line segment of length \(6\,{\text{cm}}.\)

Q.3. Find the length of the line segment \(AB,\) whose coordinates of \(A\left({3,4} \right)\) and \(B\left({2,0} \right).\)
Ans: Given coordinates are \(A\left({3,4} \right)\) and \(B\left({2,0} \right)\)
We know that distance between two points \(\left({{x_1},{y_1}}\right)\) and \(\left({{x_2},{y_2}}\right)\) is \(\sqrt {{{\left({{x_2} – {x_1}} \right)}^2} + {{\left({{y_2} – {y_1}} \right)}^2}} \)
\( \Rightarrow AB = {\sqrt {{{\left({2 – 3} \right)}^2} + \left({0 – 4} \right)} ^2}\)
\( \Rightarrow AB = \sqrt {{{\left({ – 1} \right)}^2} + {{\left({ – 4} \right)}^2}} \)
\( \Rightarrow AB = \sqrt {1 + 16} \)
\( \Rightarrow AB = \sqrt {17} \)
Hence, the length of the given line segment is \(\sqrt {17} \,{\text{units}}.\)

Q.4. Identify the given figure as a line, line segment or a ray.

Ans: We know that the line segment connects any points on the line. The line has no endpoints, it can extend infinitely in both directions, but the line segment has a fixed length in between two points. Given figure is a line as it has extended infinitely in both directions. And, the portion of the line in between points \(A\) and \(B\) is called the line segment.

Q.5. Find the length of the line segment drawn between the points \(\left({4,0} \right)\) and \(\left({0,3} \right).\)
Ans: We know that distance between two points \(\left({{x_1},{y_1}} \right)\) and \(\left({{x_2},{y_2}} \right)\) is \(\sqrt {{{\left({{x_2} – {x_1}} \right)}^2} + {{\left({{y_2} – {y_1}} \right)}^2}} \)
The distance between the points \(\left({4,0} \right)\) and \(\left({0,3} \right).\)is given by
\(\sqrt {{{\left({0 – 4} \right)}^2} + {{\left({3 – 0} \right)}^2}} \)
\( = \sqrt {{{\left({ – 4}\right)}^2} + {{\left( 3 \right)}^2}} \)
\( = \sqrt {16 + 9} = \sqrt {25} = 5\)
Hence, the length of the line segment drawn between the points \(\left({4,0} \right)\) and \(\left({0,3} \right)\) is \(5\,{\text{units}}.\)

Summary

In this article, we have studied the definitions of line and the line segment, which is the part of the line with a fixed length. The symbols used for line segment mathematically and diagrammatically are also shown in this article.

Here, we also studied the methods of measuring the line segments, such as the observation method, by using trace paper and by using the ruler and compass. We also studied the construction of line segments by using the ruler only and also by using a ruler and compass with the help of solved examples. We also discussed the differences between the line segment and the line and also discussed the difference between a line segment and a ray.

FAQs

Q.1. Find the length of the line segment joining the points?
Ans: The length of the line segment joining the two points \(\left({{x_1},{y_1}}\right)\) and \(\left({{x_2},{y_2}}\right)\) is given by \(\sqrt {{{\left({{x_2} – {x_1}} \right)}^2} + {{\left({{y_2} -{y_1}} \right)}^2}} \)

Q.2. What is the line segment in Math?
Ans: In math, the line segment is a part of the line with a fixed length. The line drawn between two fixed points is called the line segment.

Q.3. What is the symbol of line segment used?
Ans: The line segment joined the two endpoints, \(A\) and \(B,\) is denoted by the bar symbol \(\left( – \right)\) such as \(\overline {AB} .\)

Q.4 How is a line segment different from a line?
Ans: The line extends infinitely in both directions, and the line segment is of fixed length.

Q.5. What are the examples of line segments in real life?
Ans: The real-life examples of the line segments are ruler, scale, sides of the polygon etc.

We hope this detailed article on the concept of line segment helped you in your studies. If you have any doubts, queries or suggestions regarding this article, feel to ask us in the comment section and we will be more than happy to assist you. Happy learning!