Types of Lines
Line is a one-dimensional geometric shape, which lays the foundation of two and three-dimensional geometry. A line can be defined as “a breadthless length”, which is the definition according to Euclid. We can see a lot of different types of lines around us in the real world, from railway tracks to crossroads on the highway, we can see the use of lines around us. In this article, we will deal with different types of lines, such as straight, curved, horizontal, vertical, parallel, intersecting, bisecting, and transversal as well. We will also learn about some special lines such as tangents, secants, and lines of symmetry. So let’s start out learning about the lines and their different types.
What is a Line?
Line is the combination of infinite points that extend to infinity in both directions. In Euclidean geometry, we define the line as, a one-dimensional shape i.e., a length without any breadth. As lines can be extended indefinitely, it has no endpoints and it also has infinity length as well. It is generally represented by a straight line with arrowheads on both ends where the arrowhead represents the indefinite extension.
What is Ray?
The term “Ray” in geometry is used to describe a specific type of line i.e., a straight line that can extend infinitely in one direction and the other endpoint is fixed. As a ray can be extended infinitely from one side, its had no defined length. For example, if A is the endpoint and B is a point in the direction of the ray, it can be denoted as “ray AB” or simply “ray A”.
What is Line Segment?
The segments of a line having two endpoints are called the line segments. In other words, a line segment is a fractional part of a line and it is generally represented by any two points lying on the line with each point having some alphabetical name. For example, if two endpoints of line segments are A and B, then the line segment can be written just as AB.
Difference Between Ray, Line Segment, and Line
The key difference between ray, line segment, and line is listed as follows:
|
Property |
Ray |
Line Segment |
Line |
|
Definition |
A portion of a line with one endpoint that extends infinitely in one direction |
A portion of a line with two endpoints |
A straight path of infinite length. |
|
Length |
Infinite |
Finite |
Infinite |
|
Direction |
Extends in one direction |
Defined by two endpoints |
Extends in both directions |
|
Endpoints |
One endpoint |
Two endpoints |
No endpoints |
|
Naming |
Named by the endpoint and any other point on the ray |
Named by the two endpoints |
Named by a single alphabet generally lowercase. |
|
Representation |
Represented by a starting point and an arrow indicating the direction |
Represented by a line segment with two endpoints |
Represented by a line without straight endpoints |
|
Intersection |
Can intersect with other geometric figures at the endpoint or along its path |
Can intersect with other geometric figures at the endpoints or along its path |
Can intersect with other geometric figures at any point on the line. |
What are Different Types of Lines?
There are various different types of lines in geometry, having various different properties and characteristics.
- Types of Lines Based on Shape
- Straight Lines
- Curved Lines
- Zig-Zag Lines
- Broken Lines or Dash Lines
- Types of Lines Based on Orientation
- Horizontal Lines
- Vertical Lines
- Diagonal Lines
- Types of Lines Based on Intersection
- Intersecting Lines
- Bisecting Lines
- Perpendicular Lines
- Parallel Lines
- Transversal Lines
Let’s discuss these types in detail as follows:
Types of Lines Based on Shape
Based on the shape or change in direction, we can classify the lines as:
- Straight Lines
- Curved Lines
- Zig-Zag Lines
- Broken Lines or Dash Lines
Let’s discuss these types in detail.
Straight Lines
Straight Lines are those lines that do not deviate from a linear path even after extending to infinity length. These lines are characterized by having the same direction and no curvature at all. We can extend straight lines indefinitely in both directions and still, the line has the same constant slope i.e., the angle from the positive x-axis.
Curved Lines
Curved lines, on the other hand, are those lines that have a gradual change in their direction i.e., their slope changes gradually between different values. Unlike straight lines, they do not follow a linear path. Curved Lines when closed can form various different geometric objects such as circles and ellipses, and when not closed makes curvature like spirals, arc, parabola, etc.
Zig-Zag Lines
Zig-zag lines are sharply pointed collections of line segments that have a sudden change in their slope. These lines are made up of a series of connected line segments that have a positive and negative slope in alternate order. These lines resemble a sequence of “Z” or “N” shapes and form a jagged line. The major use case of Zig-zag lines is in art and graphic design, where these lines are used to represent sudden rapid change or dynamic movement.
Broken Lines
Broken lines are a collection of many tiny line segments that are arranged in a straight line, where the length of each line segment can vary depending on the use case. Broken Lines are also called dashed lines, as these line segments look like dash. These lines are used in many fields such as geometry, art and design as well as architectural drawing.
Types of Lines Based on Orientation
- Horizontal Lines
- Vertical Lines
- Diagonal Lines
Horizontal Lines
Horizontal lines are those lines, that are parallel to the horizontal axis i.e., the x-axis or the ground level. In other words, those lines which go from left to right or vice versa are called horizontal lines. In algebra, we can represent the horizontal lines using the equation y = constant. We can see the horizontal lines in the real world in infrastructure or buildings.
Vertical Lines
Vertical lines are opposite to the horizontal lines and are parallel to the verticle axis i.e., the y-axis. In other words, those lines which are perpendicular to the ground level are called vertical lines. These lines go in the up and down direction and we can see these lines in the real world as poles, multi-floor buildings, columns to support structures, etc.
Diagonal Lines
Diagonal lines are lines which are neither go in a horizontal direction nor in a vertical direction as these lines are at that slant whose slope lies between horizontal and vertical. Other than diagonal lines, these are called oblique lines as well.
Types of Lines Based on Intersection
- Intersecting Lines
- Bisecting Lines
- Perpendicular Lines
- Parallel Lines
- Transversal Lines
Intersecting Lines
Intersecting lines are two or more lines that meet or cross or intersect at a common point. The point where these lines meet is called the intersection point. In algebra, this point of intersection is a solution to the system of equations formed by the two lines.
Bisecting Lines
Bisecting lines are those lines that divide an object i.e., an angle, triangle, any polygon; or a line segment into two equal parts. They pass through the midpoint of the object i.e., the median; for triangles or the line segment, dividing it into two congruent halves. Bisecting lines are commonly used in geometry to divide angles or line segments equally.
Perpendicular Lines
Perpendicular lines are those intersecting lines that make a right angle i.e., 90o, with each other. One such pair of perpendicular lines are vertical and horizontal lines if they intersect. Also, the slope of perpendicular lines has a relationship with each other i.e., a product of the slope of perpendicular lines is always -1. For example, if one line has a slope of 2, the perpendicular line will have a slope of -1/2.
Parallel Lines
On the other hand, parallel lines are the opposite of intersecting lines i.e., they never intersect, no matter how far they are extended. Due to this they always maintain the same distance between them. Other than all these properties, all the parallel lines have the same slope but different y-intercepts. In algebra, all the parallel lines have similar equations except the constant part. For example, the lines y = 2x + 1 and y = 2x – 3 are parallel.
Transversal Lines
Transversal lines are those lines that intersect two or more other lines. For two lines, transversal lines form 8 angles and in the case of parallel lines, these 8 angles show various properties and relationships. Some of these angles are corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. In geometry, transversal lines are generally studied in relation to parallel lines only but that is not the only case.
Special Types of Lines
There are various special types of lines in geometry, some of these lines are:
- Tangent Lines
- Secant Lines
- Skew Lines
- Lines of Symmetry
These special types are discussed in detail as follows:
Tangent Lines
Tangent lines are very important lines in geometry and calculus and are defined as those lines which only touch the curve or geometric object at one point and then never intersect again. At the point of contact tangent and curve have the same slope i.e., dy/dx if y=f(x) is the given curve. In the case of two dimensions, a tangent of any curve at any point represents the instantaneous rate of change which is the same as the slope.
Secant lines
On the other hand, secant lines are different than tangent as these lines intersect the curve or geometric object such as a circle at two or more distinct points. There are some properties of secant lines with respect to the circle which is called “tangent secant theorem” and “alternate secant theorem”.
Skew Lines
All the lines we have discussed till now are generally discussed in two dimensions only but skew lines are not defined for two dimensions. In three-dimensional space, skew lines are those pair of lines that neither intersect nor parallel to each other.
Line of Symmetry
A line of symmetry is the line that divides a shape into two congruent halves i.e., two halves with each being the mirror image of the other. Due to this fact, the line of symmetry is also called a mirror line. In other words, a line of symmetry is that line, along which if a shape is folded both halves overlap each other perfectly. This concept is applied to various geometric shapes, including polygons, letters, and objects.
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FAQs on Types of Lines
Q1: Define Line.
Answer:
A line is a straight path that extends infinitely in both directions. It has no endpoints and is often represented using a straight line with arrows at both ends. A line can be thought of as a collection of points that extend indefinitely in both directions.
Q2: Define Ray.
Answer:
A ray is a straight line that extends infinitely in one direction from a specific starting point called the endpoint. It has no defined endpoint in the other direction and continues indefinitely.
Q3: Define Line Segment.
Answer:
A line segment is a straight path between two points in space. It consists of the endpoints and all the points lying between them. Unlike a line, a line segment has a defined length and can be measured.
Q4: How many Types of Lines in Geometry?
Answer:
There are various types of lines, based on various different parameters. Some of these types are as follows:
- Types of Lines Based on Shape
- Straight Lines
- Curved Lines
- Zig-Zag Lines
- Broken Lines or Dash Lines
- Types of Lines Based on Orientation
- Horizontal Lines
- Vertical Lines
- Diagonal Lines
- Types of Lines Based on Intersection
- Intersecting Lines
- Bisecting Lines
- Perpendicular Lines
- Parallel Lines
- Transversal Lines
Q5: What is a Perpendicular Line?
Answer:
A perpendicular line is a line that forms a 90-degree angle with another line or surface. If two lines intersect and the angles formed are all 90 degrees, they are said to be perpendicular to each other.
Q6: What is a Parallel Line?
Answer:
Parallel lines are lines that lie in the same plane and never intersect, no matter how far they are extended. They have the same slope and will always maintain the same distance apart.
Q7: Do the Parallel Lines Meet?
Answer:
No, parallel lines never meets, even we extend those lines to infinite distance then also they never meet.
Q8: What is an Intersecting Line?
Answer:
An intersecting line is a line that crosses or meets another line at a specific point called the point of intersection. When two lines intersect, they share a common point.
Q9: What is a Transversal Line?
Answer:
A transversal line is a line that intersects two or more other lines at different points. It forms various angles with the intersected lines, such as corresponding angles, alternate interior angles, and alternate exterior angles.
Q10: What is a Skew Line?
Answer:
Skew lines are lines that do not lie in the same plane and are neither parallel nor intersecting. They are non-coplanar lines that maintain a constant distance between each other while moving in space.
Q11: What is a Tangent Line?
Answer:
A tangent line is a line that touches a curve or surface at a single point and does not intersect it further. It represents the instantaneous direction of the curve at that point.