Introduction to Lines
Everything in the world right from a small flower to an area in the map is made up of a set of dots put together in various forms. The most basic and elementary form of geometry is the line.
It is a one-dimensional figure having no thickness and extending infinitely from the extreme ends. It is also known as a straight line, or a right to emphasize the fact that it does not have any curves anywhere along its length. They have the ability to be embedded in higher dimensional spaces.
In Ancient time, Mathematicians introduced the concept of a line with the sole purpose of denoting objects which had no curves or were straight with negligible depth and breadth. Famous mathematician defined the line is "breadthless length".
A line has a start and an endpoint. Let's say the points are A and B.
We represent a line by placing two arrows at both endpoints pointing in opposite directions. It symbolizes the fact that the line is extending in both directions.
Types of Lines
There are various types of lines. Let us discuss the formulae, figures, and definitions of each one of it.
There are five types of lines, they are:
Vertical line
Horizontal line
Parallel line
Skew line
Perpendicular lines
Vertical Line
A vertical line is a straight line, or in layman’s terms, a standing line. This type of line has an undefined slope.
We can draw a graph for a vertical line by plotting x = n. Here, n is equivalent to any sort of real number. All points in the vertical line have the same x coordinate. It is parallel to the y-axis of the coordinate plane.
The equation of the vertical line is, x = a. Here x is any point in the line of coordinate x, and a is the x-intercept.
Horizontal Line
A horizontal line is one of the types of lines in which all points have the same y - coordinate. It is also called a sleeping line. It is parallel to the x-axis of the plane. The slope of the horizontal line is zero.
The horizontal line equation is y = b. Here y is any point in the line of x coordinates, and b is the y-intercept. It is independent of x.
Parallel Line
Two lines are said to be parallel when the distance between the two straight lines is the same at all points. These two lines do not intercept at any point in space. They never meet at any point.
Perpendicular Line
Perpendicular lines are formed when a horizontal and a vertical line meet each other at a point. They are two lines that form a congruent adjacent angle to each other. The angle formed between the vertical and the horizontal line is ninety degrees.
Some Basic Definitions
Line segment: A line segment has two endpoints with a fixed length.
Ray: A ray has one endpoint, and the other end infinitely extends in one direction.
Straight line: A straight line has neither a start nor an endpoint and is of infinite length.
The Equation of a Line
The standard form of line equation is Ax + By = C where A, B, and C are real numbers, A > 0 and x, y are variables. The standard form of line equation can also be written as Ax + By - C = 0.
Standard Form of Equation of a Line
The standard form of a line is in the form Ax + By = C, where A, B, and C are integers, it gives all of the same information as the slope-intercept form, y = mx + c.
The equation of a straight line parallel to the x-axis
The line y = k is parallel to the x-axis lies above or below the x-axis according to k which is positive or negative.
The equation of the straight line parallel to the x-axis is independent of x.
The equation of a straight line parallel to the y-axis
The line x = k is parallel to the y-axis lies right or left of the y-axis according to whether k is positive or negative. The equation of the straight line that is parallel to the y-axis is independent of y.
The slope-intercept form
The equation of a straight line is y = mx + c. It has a slope ‘m’ and makes an intercept c on the y-axis.
The Point-Slope Equation of a Line
The equation of a straight line passing through a fixed point and having a given slope m is called a point-slope form.
(y−y1)= m(x−x1), is the general equation of the straight line passing through the fixed point (x1, y1) and having slope m.
The equation of Line from Two Points
The equation of a straight line going through two fixed points is also called a two-point form.
(y−y1)= m(x−x1) is the general equation of a straight line passing through the fixed points (x1, y1), (x2, y2) and having slope m.
where, \[m = y_{2} - y_{1}/x_{2} - x_{1}\]
FAQs on Lines
1. What is a Line?
A single dimensional figure without any thickness and extendable in both directions is called a line. A line is straight without any curves and zigzags, it is described as a right and straight line. Most lines are considered as one-dimensional objects but can be embedded in different dimensional spaces. It has two points and has a finite length, but can be extended infinitely in both directions.
"Euclid defined a line as a "breadthless length," and a straight line as a line that "lies evenly with the points on itself" (Kline 1956, Dunham 1990)"
When two lines extend in the same direction without intersecting each other are called parallel lines but when two lines extend in opposite directions without intersecting each other are called skew lines.
2. What are the 7 kinds of Lines?
There are different types of lines used by students and artists to create shapes and art pieces with their imagination power. From geometry to art lines are used in different ways and there are different kinds of lines like thick, thin, horizontal, vertical, zigzag, diagonal, and curly which are said to be 7 different kinds of lines. Artists use lines to express their feelings in the art pieces they create. Lines are said to be the basic tool of artists but various artists use lines differently, some lines are expressive, some lines are hidden as you can see only drawn objects and not the line.
3. How many types of basic Lines are there?
There are so many types of lines in different fields and subjects. But in Geometry, there are two basic types of lines called straight lines and curved lines. Apart from that, we can find lines everywhere in our daily life and derived from a set of two points extendable in both directions. A line is an independent object and is used to create different shapes.
The different types of lines are as mentioned below:
1. Straight line
2. Curved line
3. Horizontal line
4. Vertical line
5. Parallel lines
6. Intersecting lines
7. Perpendicular lines
8. Transversal line
4. What are Lines in Math?
A set of two points that can be extended infinitely in two opposite directions having no thickness and length is called a line in mathematical terms. A line is often explained as the shortest distance between two points, for example, A and B are two points and the distance between point A and Point B measured after connecting them with a straight figure is called a line. While drawing a line in Math (Geometry) arrows are used at both points to indicate that the line is extendable infinitely in both directions.