Line Segments and Ray: Definitions, Properties, and Examples

You have landed on the right page to learn about Line Segments and Ray. Geometry is the study of the position, shape, size, and other properties of different figures. But before we dive deep into learning geometrical figures, it becomes essential for us to learn the basic concepts of geometry. Geometrical terms such as point, line, plane, etc., are the basic concepts for developing geometry.

A point is an exact location that does not have length, width, or thickness. A part of a line with two distinct endpoints is called a line segment, and a ray is a part of a line with just one endpoint. Let us learn about line segments and rays in detail from this article.

Point, Line, Line Segment, and Ray

Point: A point shows a definite position or location, which cannot be moved. A dot(.) represents it. It is made with a sharp pencil on a sheet of paper.

A point has no length, no breadth, and no thickness. Points are named using single capital letters.
Points can be physically represented by the head or tip of a drawing pin, the tip of a sharp needle, etc.

Line: A collection of points make a line. It extends endlessly and indefinitely in both directions. Therefore, we always draw a line with arrows at both ends. A line has no endpoints. So, it has no beginning and no end, and thus its length cannot be measured.

A line can be named in \(2\) ways.
1. By using a single small letter, for example, line \(p\).
2. By using any two points marked on it. For example, line \(AB\) or \(\mathop {AB}\limits^ \leftrightarrow .\)
3. The \(2\) arrows of a line drawn in opposite directions indicate that a line has unlimited length, i.e., it can be extended up to any distance on either side.

4. A line may be straight or curved, but when we say “a line”, it generally means a straight line. The basic idea of a line is its straightness and that it extends indefinitely in both directions.

5. An unlimited number of lines can be drawn through a given fixed point. The below-given figure shows a fixed point \(A\). It is clear from the figure that an unlimited number of lines can be drawn through \(A\).

6. One and only one line can be drawn through any two fixed points. In the below-given figure, \(A\) and \(B\) are \(2\) fixed points. It is clear from the figure that only one line can be drawn through the fixed points \(A\) and \(B\).

7. Every line has an infinite or uncountable number of points in it.

Line Segment: A part of the line is called a line segment. It has \(2\) endpoints and has a definite length, which cannot be increased or decreased. Line segment \(AB\) can be written as \(\overline {AB} \).

Physically, the edge of a table, the edge of a ruler, the edge of a blackboard, etc., represents line segments.

Ray: A ray is a part of a line with one endpoint and can be extended infinitely in the other direction. The fixed endpoint is called the initial point of the ray. The length of the ray cannot be measured. Ray \(AB\) can be written as \(\overrightarrow {AB} \).

1. A ray has only one end or fixed point, which is also known as its initial point.
2. A ray extends infinitely in only one direction.
3. An unlimited number of rays can be drawn with the same initial point.
4. A ray is a part of a line.

Difference Between Line, Line Segment, and Ray

We have already learnt the definitions and explanations of basic concepts of geometrical figures, like point, line, ray, line segment, etc. Let us further point out some differences between line, line segment, and ray. Below are some of the points listed out.

Solved Examples – Line Segments and Ray

Q.1. Name the following:
a) All the lines that are shown in figure 1.
b) All the rays that are shown in figure 2.

Ans: a) We always draw a line with arrows at both ends. Hence, the lines shown in figure 1 are \(AB,\,CD\) and \(EF\).
b) A ray is part of a line with one endpoint and can be extended indefinitely in the other direction. Hence, the rays shown in figure 2 are \(AB\), and \(CD\).

Q.2. Correct the statement if it is wrong.
a) A ray has a definite length.
b) A line segment has a definite length.
c) A ray has only one endpoint.
d) A ray can be extended infinitely on both sides.
Ans: a) A ray has a definite length \(\Rightarrow\) The statement is not correct.
The correct statement is; A ray has an indefinite length because the ray is a part of a line with one endpoint and extended indefinitely in the other direction.
b) A line segment has a definite length \(\Rightarrow\) This statement is true
c) A ray has only one endpoint \(\Rightarrow\) This statement is true
d) A ray can be extended infinitely on both sides \(\Rightarrow\) The statement is incorrect.
The correct statement is; A ray can be extended infinitely only in one direction.

Q.3. How many lines can be drawn, passing through:
a) A given point
b) Two given fixed points
Ans: A collection of points makes a line.
a) A given point: Through a given point, we can draw infinite lines.
b) Two given fixed points: Through two given fixed points, we can draw only one line.

Q.4. Does a line segment go on forever?
Ans: Although a line segment is a part of a line, it cannot go on forever as it has two endpoints.

Q.5. From the below-given figure, identify whether \(SG,\,SF,\,SE,\,SD,\,SC,\,SB\) and \(SA\) are line, line segments, or ray?

Ans: The given figure shows a point of source of light \(S\). \(SG,\,SF,\,SE,\,SD,\,SC,\,SB,\) and \(SA\) are rays of light starting from the source \(S\). As, \(S\) is the fixed point, and the other end can extend indefinitely \(SG,\,SF,\,SE,\,SD,\,SC,\,SB,\) and \(SA\) are rays.

Summary

This article taught us the basic geometrical terms, i.e., point, ray, line, and a line segment. We emphasized the learning of line segment and a ray more and had detailed learning on these terms. We also learnt about the difference between ray, line, and line segment, and lastly, we solved some examples to strengthen our grip over the concept.

Learn How to Measure Line Segments

Frequently Asked Questions

Q.1. How are a line segment and a ray the same?
Ans: A line segment is a part of a line with two endpoints, whereas a ray is also a part of a line that has \(1\) endpoint and extends indefinitely in one direction. So, a line segment and a ray both are part of a line.

Q.2. What are a line, ray, and segment?
Ans: Line: A collection of points make a line. It extends endlessly and indefinitely in both directions.
Ray: A ray is part of a line with one endpoint and can be extended indefinitely in the other direction.
Segment: A part of the line is called a line segment. It has \(2\) endpoints and has a definite length, which cannot be increased or decreased.

Q.3. What is the difference between ray and line segment?
Ans: A ray and a line segment both are a part of a line. The only major difference between them is that a line segment has two endpoints and thus cannot be extended in both directions and has a fixed length. In contrast, a ray has one point fixed and the other endpoint extended indefinitely in one direction.

Q.4. Can a line segment also be a ray?
Ans: A line segment and a ray both are a part of a line. A line segment has two endpoints, whereas a ray has only one endpoint. So a line segment cannot be a ray, but it can be a part of a ray.

Q.5. Out of a line, line segment, and a ray, which has one fixed endpoint?
Ans: As the definition says, a line has no endpoints and can thus be extended in either direction. A line segment is a part of a line whose both endpoints are fixed and definite in length. A ray is also a part of a line that has one fixed endpoint, and the other endpoint can be extended in the other direction indefinitely. Hence, we can say that a ray has one fixed endpoint out of a line, line segment, and a ray.

We hope this detailed article on line segments and ray 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!