Lines in Geometry, Types, Solved Examples

Different Types of Lines: A line is defined by its length but not by its breadth. A line is a two-dimensional geometric figure that may travel in any direction. There are an infinite number of points that make up a line. On all sides, it is endless and has no end. A line is a two-dimensional object. Ancient mathematicians established the concept of a line or straight line in geometry to depict straight objects with little breadth and depth. It’s frequently explained in terms of two points.

In the notion of analytic geometry, a line in the plane is commonly described as a collection of points whose coordinates fulfil a certain linear equation; however, in the concept of incidence geometry, a line can be an independent entity, separate from the set of points that lie on it. For example, the railway track, chessboard, scissors, quadrilateral, the corners of the wall, the English alphabet L, our kitchen tiles, the hands of a clock, sides of a polygon, pencil, and set squares blackboard, etc. have lines in it. On this page, we will learn everything about Line and its types. Read further to find more.

Lines in Geometry

Let us learn about something which we do in our school, forming lines. When you are moving to your classes after the school assembly, you must move in a line.

When you are in a line, and your friend cuts the line to stand behind you, will it affect the line?

No.

Because a line can have an infinite number of points.

What is a Line?

Definition: A line is a set of points in a straight path that extends in opposite directions without an end.
In other words, a line is a type of geometrical shape that can extend in both directions. A line is made up of a countless number of points. It is infinite and has no ends on both sides. A line is one-dimensional and has length but no width.
A line through two points \(A\) and \(B\) is written as \(AB\) or \(BA.\) Also, it is denoted by the letter ‘ \(l\)’.

A line segment has two endpoints. If we extend the two endpoints in either direction endlessly, we get a line. 

Here, \(AB\) is the line segment.
A ray is a portion of a line starting at a point and going in one direction endlessly.

In the picture above, \(\overrightarrow {AB} \) is a ray.

Types of Lines

There are different types of lines in geometry. Lines can be said as the foundation of geometry. Let us discuss different types of lines with examples.

Straight Line

A straight line is a line with no curves.

Straight lines are further classified into horizontal lines (sleeping lines), vertical lines (standing lines), and oblique lines (slanting lines). 

Horizontal Line

A line that is parallel to \(X\)-axis is called a horizontal line. This line does not touch any point on the \(X\)-axis. All the points on this line will have the same \(y\)-coordinate.

Here, the lines \(l,m,\) and \(n\) are the horizontal lines.
Real-life examples of horizontal lines are edges of the saffron, white, and green stripes in the Indian flag, the edges of the steps on the staircase, edges of the planks on the railway tracks, etc.

Vertical Line

A line that is parallel to \(Y\) -axis is called a vertical line. It goes straight up and down, parallel to the \(Y\)-axis in the coordinate plane. All the points on this line will have the same \(x\)-coordinate.

Real-life examples of vertical lines are the row of pillars as shown below, a row of tall trees on a highway, electric poles placed on the roads, etc. 

Oblique Line

A straight line that is neither horizontal nor vertical is called an oblique line or a slanting line.

When two or more lines are used together, they form different types of lines like parallel lines, perpendicular lines, and transversal lines, etc. Let us discuss them in detail. 

1. Parallel Lines

Two lines that do not meet at a point in a plane surface are parallel to each other. Lines that do not cross each other or intersect at a point are parallel lines. It is denoted as \(\parallel .\)

Here, line \(l\) is parallel to line \(m\). We can write it as \(l{\rm{ }}||{\rm{ }}m\).
Real-life examples of parallel lines are the roads, bridges, railway tracks, walls of buildings, the stack of identical notebooks, a collection of same-sized papers when arranged uniformly, etc.

2. Intersecting Lines

When two or more lines intersect each other in a plane, then they are called intersecting lines. Intersecting lines are two lines that cross exactly at one point. This shared point is called the point of intersection.

Here, the lines \(l\) and \(m\) are intersecting lines.
Real-life examples of intersecting lines are the two blades of the scissors, signboards on the roads are one of the best examples to show the intersection of lines. 

3. Perpendicular Lines

Two lines are said to be perpendicular if they intersect such that the angle formed between them is a right angle. In the figure, the lines \(l\) and \(m\) are perpendiculars. Symbolically it is written as \(l \bot m\).

Real-life examples of perpendicular lines are the poles of a football goal post, the poles on an electric post, the edges of a notebook or textbook, etc.

The English alphabet T, edges of set squares, blackboards, television sets, bookshelves, etc., are also examples of perpendicular lines. 

4. Transversal Lines

The transversal line is a straight line that cuts two or more lines that may or may not be parallel. In geometry, a transversal line passes through two lines in the same plane at two distinct points. 

Here, line \(n\) is the transversal line.
Real-life examples of transversal lines are the antenna, stair railings, roof ceilings, etc.

5. Skew Lines

In three-dimensional geometry, skew lines are two lines that do not intersect and are not parallel.

The lines \(l\) and \(m\) are examples of two skew lines for each figure. 
Some examples to help you better visualize skew lines are the roads or flyovers along highways or cities. Since the roads are considered separate planes, lines found in each will never meet or nor parallel to each other.

The roller coaster rides and pipeline connections in buildings are examples of skew lines.

6. Coplanar Lines

In three-dimensional geometry, coplanar lines are two lines that lie in the same plane.

The lines \(l\) and \(m\) in the figure are in the same plane; hence they are coplanar.
Real-life examples of coplanar lines are the planks in a railway line, rail in a staircase, markings on the road, markings on a cricket or football ground.

7. Concurrent Lines

A set of three or more lines in a plane that intersect each other in exactly one point or which pass through the same point are called concurrent lines. The common point is called the point of concurrency.

Here, the point \(P\) is called the point of concurrency.
Real-life examples of concurrent lines are bicycle rims, hands of a clock, etc.

8. Tangent Lines

A straight line that touches a curve but does not cross it.

9. Secant Line

In geometry, a secant line is a line that intersects the curve at a minimum of two distinct points.

Solved Examples on Types of Lines

Let us understand different types of lines facts with questions.

Q.1. Identify different types of lines?
(i)

(ii)

(iii)

Ans: (i) We can see that three lines are meeting at a common point. Hence, it is a concurrent line.
(ii) We can see that one line is intersecting the other two lines at distinct points. Hence it is a transversal line.
(iii) We can see that two lines are meeting each other. Hence it is an intersecting line.

Q.2. How many lines can pass through two given points??
Ans: Let us consider two points \(A\) and \(B\) and draw a line \(l\) passing through the points.

We can observe that only one line can pass through two given points.

Q.3. Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.

Ans: The twelve possible ways of naming the lines choosing two letters at a time is given by \(AB,\,BA,\,AC,\,CA,\,AD,\,DA,\,BC,\,CB,\,BD,\,DB,\,CD,\,DC\)

Q.4. Use the figure to name four rays.

Ans: We know that a ray is a portion of a line starting at a point and going in one direction endlessly. In the given figure, the four rays are \(\overrightarrow {OB} ,\overrightarrow {OC} ,\overrightarrow {OD} \) and \(\overrightarrow {ED} \)

Q.5. Identify the skew lines.

Ans: We know that skew lines are two lines that do not intersect and are not parallel.
Hence, the skew lines are \((r,{\rm{ }}l),(r,{\rm{ }}m),(r,{\rm{ }}p)\) and \((r,{\rm{ }}q)\)

Summary

From this article, we have got a brief knowledge about the line and the important aspects of lines. With the different types of lines notes introduced in this blog, we will be able to apply the concepts to real-life applications and explore more exciting facts about the line.

Frequently Asked Questions on Lines

Q.1. What are the two types of lines in \(3\)- dimensional geometry?
Ans: In \(3\)-dimensional geometry, the two types of lines are skew lines and coplanar lines.

Q.2. What is a vertical line?
Ans: The line that is parallel to \(y\) -axis is called a vertical line.

Q.3. What is a line?
Ans: A line is a set of points in a straight path that extends in opposite directions without an end.

Q.4. What are the \(12\) types of lines?
Ans: The \(12\) types of lines are horizontal, vertical, parallel, perpendicular, tangent, secant, concurrent, skew, coplanar, oblique, tangent, and intersecting lines.

Q.5. What is a horizontal line?
Ans: The line that is parallel to \(x\)-axis is called a horizontal line.