Line: Definition, Diagrams, Types and Examples

In geometry, it is common to say a line segment and lines are the same. A Line segment has a definite beginning and a definite end, but a line is extended towards infinity at both ends. Examples of line segments include the length of a table, the distance of a straight road, etc. A segment is part of a line, but a line is not part of a segment. Let’s learn about lines, their types and some real-life examples.

Horizontal, vertical lines, parallel and perpendicular lines are examples of different types of lines. A line is a one-dimensional figure, which has length but no width. A line is made up of a series of points that are infinitely stretched in opposite directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line. Continue reading this article to know more about Line.

What is Line?

A line has a length but no width. A line is a type of geometric diagram that can move in both directions. So, it is made up of an endless number of points, and it is infinite and has no ends on both sides. A line is one-dimensional.

In geometry, the ancient mathematicians introduced the notion of the line or straight line to display linear objects having nominal width and depth. It is described in terms of two points. For example \(\overleftrightarrow {PQ}.\)

Definition of Line Segment

In mathematics, line segment and line are essential concepts for constructing geometrical shapes. In geometry, a 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 size.

As per Euclid’s concept, a line is a breadthless length. A line is an essential geometric figure, which connects all points on it. A line has no endpoints, and it extends infinitely in both directions. A line segment is a part of the line. A line segment connects any of the 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 connected way of the two points, which you can measure. Line segments are utilised to form the sides of the polygon.

Types of Lines

In geometry, we use different types of lines. Lines are the foundation of geometry. We have two types of lines, and they are given below:

Straight lines are classified as:
a) Horizontal lines or the sleeping lines,
b) Vertical lines or the standing lines and
c) Oblique lines or slanting lines.

The general equation of the straight line is as given \(ax + by + c = 0.\)

Horizontal Lines

Lines that are parallel to the \(x-\)axis are known as horizontal lines.

An example of the horizontal line is shown below:

The staircase is one of the examples of horizontal lines. Other examples include steps on the planks on railway tracks.

Vertical Lines

Lines that are parallel to \(y-\)axis is known as vertical lines. This line goes straight up and down, similar to the \(y-\)axis of the coordinate plane.

An example of the vertical line is shown below:

The bamboo sticks in the fence is an example of vertical lines. The row of tall trees on a highway, Electric poles are a few examples of vertical lines.

Other Types of Lines

When two or more lines are placed together, they form various lines like parallel lines, perpendicular lines, and transversal lines.

Parallel Lines

The two lines are shown below, which we can name as \(l\) and \(m\) in the same plane are parallel lines if they do not intersect when produced indefinitely in either direction, and we write \(l\parallel m\) which is read as \(l\) is similar to \(m\).

Clearly, when \(l\parallel m\), we have \(m\parallel l.\)
An example of the real-life of parallel lines is shown below:

Railway tracks are the perfect example to represent the parallel lines. Walls of buildings, a stack of identical notebooks, collection of same-sized papers are all parallel to each item in the group when arranged uniformly.

Intersecting Lines

Two non-parallel lines can meet at the same point, and those lines are known as intersecting lines. Intersecting lines are the two lines that share exactly one point. This shared point is called the point of intersection.

An example of real-life Intersecting lines is shown below:

Scissors, the two blades of the scissors intersect each other to make it work effectively. The signboards on the roads are one of the best examples to show the intersection of lines.

Transversal Lines

A line that is intersecting two or more given lines in a plane at different points is known as the transversal to the given lines.

An example of the real-life transversal line is shown below:

These are some examples of transversal lines in our daily life, like the antenna, stair railings, etc. Apart from these, there are few more types of lines, such as skew lines, coplanar lines, concurrent lines, etc.

Perpendicular Lines

A line is perpendicular to another line if the two lines intersect at a right angle. The symbol of \((⊥)\) denotes perpendicular lines. This property of being perpendicular is the relationship between the two lines that meet at a right angle (\(90\) degrees).

A real-life example of perpendicular lines is shown below:

Set squares, blackboards are also real-life examples of perpendicular lines. Television sets, bookshelves, and the globe, where latitude and longitude intersect, are all examples of perpendicular lines. 

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Differences Between Line and Line Segment

Line segment connects any points on the line. There are no endpoints on the line, 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	The 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 displayed 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: \(\overline {CD} \)

Importance of Lines

One of the most fundamental elements of art is the line. An essential feature of a line is that it indicates the edge of a two-dimensional (flat) shape or a three-dimensional form. A shape can be shown utilising an outline, and contour lines can indicate a three-dimensional structure.

Lines are used to create shape, pattern, texture\(+\), space, movement and optical illusion in design. The use of lines allows the artist to demonstrate delicacy or force. Curves may take us slowly uphill or turn sharply.

Solved Examples– Lines

Q 1. \(AB||CD\). Determine \(∠a\).
Ans: Through \(O\) draw, the line \(l\) parallel to both the lines \(AB\) and \(CD\).
\(∠a = ∠1 + ∠2\)
Now, \(∠1 = 55°\) [Alternate \(∠s\)]
And, \(∠2 = 38°\) [Alternate \(∠s\)]
\(∴ ∠a = 55° + 38°\)
\( ⇒ ∠a = 93°\)
Hence, \(∠a = 93°\)

Q.2. \(AB||CD\). Determine \(x\).
Ans: Through \(O\) draw, the line \(l\) parallel to both the lines \(AB\) and \(CD\).
\(∠1 = 45°\) and, \(∠2 = 30°\) [Alternate \(∠s\)]
\(∴ ∠BOC = ∠1 + ∠2\)
\( ⇒ ∠BOC = 45° + 30° = 75°\)
Clearly, \(x = {\rm{reflex}} ∠BOC\)
\(∴ x = 360 – ∠BOC\)
\(⇒ x = 360° – 75° = 285°\)
Hence, \(x = 285°\)

Q.3. Is the given figure a line, line segment or a ray?

Ans: You know that a 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 between the two points. Given diagram is the line as it has extended infinitely in both directions. And, the portion of the line in between points \(A\) and \(B\) is known as the line segment

Q.4. Give reasons why \(l_1 || l_2\). Is \(m_1 || m_2\)?
Ans: Since lines \(l_1\) and \(l_2\) are intersected by a transversal \(m_2\) such that the sum of two interior angles on the same side of the transversal is \(50° + 130° = 180°\), i.e. they are supplementary.
Therefore, \(l_1 || l_2\)
We observe in the given diagram that the lines \(m_1\) and \(m_2\) are intersected by a transversal \(l_2\) such that the alternate interior angles are equal, each being \(130°\).
Hence, \(m_1 || m_2\).

Q.5. Show that \(AB || EF\).

Ans: We have,
\(∠BCD = ∠BCE + ∠ECD\)
\( ⇒ ∠BCD = 36° + 30° = 66° \)
\(∴ ∠ABC = ∠BCD\)
Thus, lines \(AB\) and \(CD\) are intersected by the line \(BC\) such that \(∠ABC = ∠BCD\), i.e., the alternate angles are similar.
Therefore, \(AB || CD\)
Now, \(∠ECD + ∠CEF = 30° + 150° = 180°\)
This shows that the sum of the interior angles on the same side of the transversal \(CE\) is \(180°\), i.e., they are supplementary:
\(∴ EF || CD\)
We have \(AB || CD\) and \(CD || EF\)
Hence, \(AB || EF\)

Summary

In the given article, we have discussed the term line, then what a line segment is. Then we have talked about types of lines that include horizontal, vertical, parallel, perpendicular, intersecting lines and transversal lines. We glanced at the difference between the line and the line segment and examples followed by the importance of line. Finally, we have given solved examples along with a few FAQs.

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Frequently Asked Questions 

Q.1. What is a line called?
Ans: A line has a length, but it has no width. A line is a type of geometric diagram that can move in both directions. So, it is made up of an endless number of points, and it is infinite and has no ends on both sides. A line is one-dimensional.

Q.2. What are the types of lines?
Ans: The types of the lines are given below:
1. Straight lines
2. Curved lines
3. Parallel lines
4. Perpendicular lines
5. Transversal lines
6. Intersecting lines
7. Horizontal lines and
8. Vertical lines

Q.3. What figure is a line?
Ans: In geometry, a line can be defined as a straight one-dimensional figure with no thickness and endlessly in both directions. It is often defined as the shortest distance between any of the two points. Here, the two points on the line are \(P\) and \(Q\). A line segment is only the part of a line.

Q.4. How is a line formed?
Ans: A line is a figure that is made when two points are connected with the minimum distance between them, and both the ends are extended to infinity. While lines have no definite beginning or end, they are displayed in our day-to-day lives with examples such as railway tracks or theway.

Q.5. How is a line made?
Ans: The line is the path of one point moving. A line has length but no width. A line is a type of geometric figure. A line is formed with an endless number of points.

Now you are provided with all the necessary information on the concept of lines and we hope this detailed article is helpful to you. If you have any queries regarding this article, please ping us through the comment section below and we will get back to you as soon as possible.