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In geometry, points and lines are the two fundamental concepts that you need to learn before learning about different shapes and sizes. A line is a one-dimensional figure, which has length but no width. It is made of a set of infinite points. A line can be extended in opposite directions infinitely.
Let’s understand what is line and its properties and also the different types of lines.
What is Line?
A line is a straight one-dimensional figure that does not have a thickness, and it extends endlessly in both directions.
The above figure shows two lines. Both lines do not have any endpoint. The two arrows at each end signify that the line extends endlessly and is unending in both directions. The length of a line cannot be measured.
A line can also be defined as a set of collinear points connected in a one-dimensional plane.
Note:
- Three points are called colinear points when they lie on the same line.
- Two points are always collinear.
In the above figure,
- Points A, B, and C are collinear points.
- Points P, Q, and R are non-collinear points. (Points P, Q, and R are not collinear).
Representing a Line in Geometry
Lines are generally denoted by the arc over the points. The line is drawn between points A and B, extending it both sides infinitely, and it is denoted by $\overleftrightarrow{\text{AB}}$.
Properties of a Line
Following are the properties of a line.
- A line can be defined as a straight set of points that extend in opposite directions
- It has no ends in both directions(infinite)
- A line has an infinite length
- It has no thickness
- A line is a one-dimensional geometrical figure
- A line has only length, and it does not have any thickness
- A line is made up of an infinite number of points.
- If three or more points are placed on the same line, they are called collinear points.
- Intersecting lines will cross at only one point
- The lines used in the graphs are used to locate the points and have many more applications, the $x$−axis is the horizontal line, and the $y$−axis is the vertical line
What is a Line Segment?
A part of a line is called a line segment. In other words, a line segment is a straight line with two endpoints. A line segment has a fixed length and can be measured using a ruler.
The above figure shows two line segments. Both line segments have endpoints in both directions. The length of a line segment can be measured.
Representing a Line Segment in Geometry
Line segments are generally denoted by the arc without an arrow over the points. The line is drawn between points A and B and it is denoted by $\overline{\text{AB}}$.
In the above figure, $\overline{\text{AB}}$ is a line segment with two endpoints, A and B. A line segment can be measured, whereas a line cannot. The length of the line segment is the distance between the two endpoints, A and B.
Similarly, a $\overline{\text{CD}}$ is also a line segment.
What is a Ray?
A part of a line having only one endpoint (starting point) but not having an endpoint is called a ray. Since a ray extends infinitely in one direction it has an infinite length and cannot be measured.
The above figure shows two rays. Both rays have one starting point but no endpoints. The length of a ray cannot be measured.
Representing a Ray in Geometry
Rays are generally denoted by the arc with an arrow on one side over the points. The line is drawn between points A and B and it is denoted by $\overrightarrow{\text{AB}}$.
In the above figure, $\overrightarrow{\text{AB}}$ is a ray with one endpoint, A. Similar to a line, a ray cannot be measured.
Similarly, a $\overrightarrow{\text{CD}}$ is also a ray.
Line, Line Segment, Ray – A Comparison
Following a comparison between a line, a line segment, and a ray.
| Line | Line Segment | Ray |
| A line is a one-dimensional breadthless(no breadth) figure extending on both sides | A line segment is a part of a line with a fixed length | A ray is the part of the line, which starts from one point and extends in one direction |
| A line has no endpoints with infinite length | A line segment has two endpoints with a fixed length | A ray has only one endpoint and has infinite length |
| A line is represented by placing arrow marks on both sides For example, $\overleftrightarrow{\text{AB}}$ | A line segment is represented by placing the bar over the letters For example, $\overline{\text{PQ}}$ | A ray is represented by placing the arrow marks on one side For example, $\overrightarrow{\text{CD}}$ |
| A line can be extended infinitely in both the directions | A line segment can not be extended further; it lies between two points | A ray extended in one direction |
Types of Lines
There are various types of lines based on the property that holds. The different types of lines are intersecting and non-intersecting lines, parallel lines, perpendicular lines, etc.
Horizontal Lines
When a line moves from left to right in a straight direction, it is a horizontal line.
Vertical Lines
When a line runs from top to bottom in a straight direction, it is a vertical line.
Intersecting Lines
Intersecting lines are the lines that formed when they cross each other at one point. The point of intersection is the point where the lines cross each other.
Non-Intersecting Lines
The lines that do not touch or intersect each other are known as non-intersecting lines. The non-intersecting lines are called parallel lines, and the distance between them is constant.
Parallel Lines
The lines are said to be parallel if they do not intersect each other and have the same distance between them from any point of the lines. Thus, parallel lines are non-intersecting lines having a constant distance.
The railway tracks are the best example of parallel lines.
Perpendicular Lines
The lines are said to be perpendicular if they intersect each other at an angle of right angle $\left(90^{\circ} \right)$. The sides of the square and the rectangle are perpendicular lines. Perpendicular lines are intersecting lines with an angle of $90^{\circ}$.
Transversal Line
The line that intersects two or more parallel lines is called the transversal. In the image given below, the dotted line intersecting the two lines is called a transversal.
Practice Problems
- State True or False
- The horizontal line moves from left to right
- The vertical line moves from left to right
- The horizontal line moves from down to up
- The vertical line moves from down to up
- Angle between two perpendicular lines is $0^{\circ}$
- Angle between two perpendicular lines is $90^{\circ}$
- Define the following
- Line
- Line Segment
- Ray
- Collinear Points
- What are intersecting lines?
- What are parallel lines?
- What is a transversal line?
FAQs
What is a line in math geometry?
A line is a straight one-dimensional figure that does not have a thickness, and it extends endlessly in both directions.
What are the 4 characteristics of lines?
Following are the main four characteristics of lines.
a) It has no ends in both directions(infinite)
b) A line has an infinite length
c) It has no thickness
d) A line is a one-dimensional geometrical figure
Why is the line the most important element?
The line is the most important element in geometry as it forms the basis of all the angles and figures (polygons).
What is the angle between two perpendicular lines?
The angle between two perpendicular lines is $90^{\circ}$.
What are the parallel lines?
Two lines are said to be parallel lines if they lie in the same plane and never meet.
Conclusion
A line is a straight one-dimensional figure that does not have a thickness, and it extends endlessly in both directions. In geometry, the line is one of the fundamental concepts. It forms the basis of all the angles and figures (polygons).
