# Points and Line Segment – Introduction, Definitions, Differences, Types, Properties, Examples

Confused about Points and Line Segment? Don’t worry! Here we are providing the complete details regarding  Points and Line Segments. Know what is the relationship between a point and a line segment. Follow the various trips and facts to remember points and line segments. Get the information regarding definition, differences, types, and examples of points and line segments in the further sections.

## Points and Line Segment – Introduction

Before going to the deeper concepts we will know about point and line segments.

What is a Point?
A point generally depicts a location in any plane. The plane can be 2 – Dimensional, 3 – Dimensional or of any Dimension.
This is the general definition of a point. In the more modern world, the point can be considered as an element in a space. A point does not have length, width, or thickness.

Properties of a Point:

• The point will not have the length, height, shape, and size.
• Point marks as the beginning to draw the figure or shape.
• The point which is marked is labeled with capital letters.

### Types of Points

There are different types of points in our general mathematics.

Collinear Points:
One or more points lying on a straight line are known as collinear points.

In the above figure, A, B, C, and D are the points that are lying on the straight line. Hence, these points are known as collinear points.

Non-Collinear Points:
If three or more points cannot be joined with a straight line, then those points are known as non-collinear points.

In the above figure, P, Q, R, and S are the points that are not lying on the straight line. Hence, these points are known as non-collinear points

Concurrent Points:

If two or any number of straight lines meet at a single point, then that point is known as a concurrent point.
The straight lines AB, CD, EF are meeting at a point which are known as concurrent points.

What is a Line Segment?
The Line Segment is a part of a line that has some boundaries. The Line Segment is a line that may be bounded between two endpoints.

Properties of Line Segment:

• The line segment will have two endpoints and all the points are present between them.
• The representation of line segments depends on the type of line segments.
• If the line segment is closed one, then it is represented with two points.
• If the line segment is an open one, then it is represented with two arrows.

### Types of Line Segments

There are different types of line segments in our general mathematics.

Closed Line Segment:
The first one is the closed line segment. This is the line segment that is bounded between two endpoints. The endpoints are mentioned by using points. So, here the point is the element that divides a line to form a Line Segment.

Open Line Segment:
Another one is the open line segment. This is the line segment that has no endpoints. The ends of the line are mentioned by using either > or <. These explain that the line is extended on both ends. So, it is a continuing line segment that has an infinite length on both sides until it is stopped by a point.

Semi-Open Line Segment:
The last one is the semi-open line segment. This kind of line segment has one endpoint at one end and no endpoint at another end. This shows us that one end is a closed line segment and another end is an open line segment. So, it is a continuing line segment at one end and a fixed-line segment at another end that has an infinite length on one side until it is stopped by a point.

### Difference between a Point and a Line Segment

Point Line Segment
Point is an element in a space that gives the exact location in some particular space The line segment is a line that has some boundaries where every point in that line lies within the boundaries
The point has no length, width, or thickness The line segment length is indefinite and it has some thickness
Point is represented with “.” The line segment is represented with “—”
Difficult to define the length, with and thickness for a point The length of a line segment may be ranging from millimeters (mm) to Kilometers(km)

### Point and Line Segment Examples

Problem 1:
Consider CX is a line segment in a One Dimensional Plane. Where C is 0 and X is 5. Show whether 3 lies in this line segment, length of the line segment and define the type of line segment.

Solution:
Given,
CX is the given line segment where C is 0 and X is 5.
3 lies between 0 and 5. So, 3 is a point in the line segment CX such that the point is 3 places from C and 2 places from X.
The Lenght of CX is 5. It has 2 endpoints so the type of line segment is a closed line segment.

Problem 2:
x=y is a line starting from the origin in a 2 Dimensional Plane. State whether (3,3) lies on the line and check the type of line segment.

Solution:
Given,
x=y is a line segment

It is a 2 Dimensional plane. So, The point is represented as (0,0).
From the figure, we observe that line x=y passes through the point (3,3).
Therefore, (3,3) lies on the line x=y.
Here, one end of the line has a point and the other end does not. So, it is a Semi-open type of Line Segment.

Problem 3: x=0 is a line in a 2 Dimensional Plane. State whether (0,-3) lies on the line and check the type of line segment.
Solution:
Given,
x=0 is a line segment

-3 lies 3 units to the left of the origin on the line x=0.
Therefore, (0,-3) lies on the line segment x=0.
Here, both the ends of the line have no endpoints and can be extended in both directions till infinity.
So, this is an Open type of Line Segment.

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