Quadrants - A Comprehensive Guide

What are quadrants? – A descriptive analysis of mathematical graphs

Did you ever wonder what those two intersecting lines in a graph mean? Or the four divisions that form around those lines. This post will discuss the meaning, nature, and application of these mathematical features in graphs.

Graphs have several applications in real life, ranging from engineering to economics. They help provide a pictorial presentation of data in a concise form. Don’t you want to know what these quadrants mean in mathematics? Then let’s read further.

Quadrants

A quadrant is a portion of a Cartesian plane (defined with two perpendicular number lines designated as x-axis and y-axis, with origin “o” as its centre) that forms at the intersection of two axes. Quadrants help identify the positions of one or more points on a plane.

The Four Coordinate Plane Quadrants

Now let’s look at the four quadrants present in a mathematical graph.

A pair of lines (the x-axis and the y-axis) intersects each other at right angles (point O). The two axes create 4 divisions or quadrants (1/4^th of a Cartesian plane) in the Cartesian plane.

The First Quadrant lies at the top right side. Both its coordinates are positive.

The Second Quadrant lies at the top left side. Here, the x-coordinate has a negative value, and the y-coordinate possesses a positive value.

The Third Quadrant lies on the bottom left side, with both quadrants being negative.

The Fourth Quadrant is available at the bottom right side with x-coordinate as positive and y-coordinate as negative.

Origin and Sign Convention

The “origin” is the intersecting point of both the X-axis and Y-axis, dividing the axes into a pair of halves. The halves are a positive and a negative semi-axis. The origin point is labelled as “O” with the coordinates 0, 0. Even in three-dimensional graphs, the origin is the meeting point of axes x, y and z.  

The sign convention in a graph is

1. OX as positive
2. OX’ as negative
3. OY as positive
4. OY’ as negative

Both the pictures define the origin point for a graph in 2D and 3D.

How to plot points on quadrants?

A 2-D graph carries two axes within a bivariate (including two variables) x-y plot. The y-axis is vertical, and the x-axis is horizontal. A data set with two relatable data variables can provide the details to plot a graph.

The general rule stands that the numbers from the first column in the table shall lie on the x-axis. But these rules do not apply to geologists who plot such graphs.

The numbers are plotted in the graph quadrants as ordered pairs that contain two values – x and y. Ordered pairs carry numbers from the “x-axis” as the first value and numbers from the “y-axis” as the second value.

The x-value represents a point in the horizontal area of the graph, whereas; the y-value represents the vertical position.

Examples of Quadrants

Let’s look at the graph given above and consider the first point (-4, 10). You’ll find the point situated at the second quadrant of the graph’s coordinate plane. The reading indicates that the value of x here is -4, and the value of y is 10.   

Now, let’s look at the second point (7, -9). In like manner, the value of x here is 7, and the value of y is -9. In other words, the point lies in the fourth quadrant.  

Suppose we consider a point in the first quadrant like (5, 9). You’ll realize that both these points lie in the first quadrant. What do you think the value of x and y would be in this case?

You and your friends can spend some time figuring out the value of the remaining points in the graph. You’ll have fun as you get together and help each other find the value of these points. It’ll help you use your time in a more effective way.

Always remember that the first value in the sign bracket depicts the value of a point on the "x-axis". The second value represents a point on the "y-axis". In the case of three-dimensional graphs, the first, second and third values shall depict points on the x, y and z axes, respectively.

The three-dimensional graph given before has a value of (-2, 4, 5). It suggests that the value of x is -2, the value of y is 4, and the value of z is 5. The point is located in a three-dimensional space than in a two-dimensional position.

The difference between a two-dimensional graph and a three-dimensional graph is that –

1. 2D graphs carry two axes, the x-axis and the y-axis. But 3D graphs have three axes x-axis, y-axis and z-axis.

2. 2D graphs carry two values at each point, but 3D graphs have three values at each point. Each of these points lies on any one of the axes.

Conclusion

So, now we hope that the concept of quadrants is clear to you. If not, you can revise this post or your book to clarify your idea on quadrants. We wish you all the best in your endeavours. 

Frequently Asked Questions by Students

Q.1. How do you identify quadrants? 

Answer – You can identify quadrants with the first number representing a point on the x-axis and the second number representing a point on the y-axis. The positive and negative values on both the numbers can help you identify their quadrant.

First quadrant = (x, y)

Second quadrant = (-x, y)

Third quadrant = (-x, -y)

Fourth quadrant = (x, -y)

Q.2. What quadrant is sin positive?

Answer – The first quadrant includes a positive value for all trigonometric functions. But, the second quadrant in the graph is sin positive.

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