What is a Quadrant in Math?

girl at whiteboard writing math equation

Margo, math expert and Operations extraordinaire, is glad you asked! Quadrants will pop up in algebra, geometry, and more, and we can help chart a course to success.

A quadrant is the area contained by the x and y axes; thus, there are four quadrants in a graph. To explain, the two dimensional Cartesian plane is divided by the x and y axes into four quadrants. Starting in the top right corner is Quadrant I and in a counterclockwise direction you will see Quadrants II through IV.

In this tutorial, we’ll define quadrants and other relevant terms and take a look at an example of accurately identifying and plotting points using quadrants. 

Students will need to successfully navigate these quadrants for a wide range of math problems, so let’s start today’s tutorial with some important vocabulary to nail down the basics. 

Related terms to know

Cartesian plane: Also known as a coordinate plane, the cartesian plane refers to the two-dimensional x and y axes and the points plotted on them. The point where the x-axis and y-axis intersect is known as the origin, with coordinates (0,0). The Cartesian plane is helpful in being able to determine the position of a given point in a 2-D plane in relation to the origin, (0, 0). 

X axis: The horizontal axis on a graph. 

Y axis: The vertical axis on a graph. 

Each point is represented by the x-coordinate (horizontal shift) followed by the y-coordinate (vertical shift). It is written as (x, y). 

Horizontal shift: A change in x-axis value that shifts the point left or right. 

Vertical shift: A change in y-axis value that shifts the point up or down. 

How do you find quadrants?

Here’s a quick breakdown and visual of where each of the four quadrants is located. 

Quadrant I consists of positive x values and positive y values, and is shown in the top right corner of the plane. 

Quadrant II consists of negative x values and positive y values, and is shown in the top left corner of the plane.

Quadrant III consists of negative x values and negative y values, and is shown in the bottom left corner of the plane.

Quadrant IV consists of positive x values and negative y values, and is shown in the bottom right corner of the plane.

Math quadrant

Example of using quadrants

Let’s use the point point (2, -3) as an example. The x-coordinate is 2, which means a horizontal shift of 2 units to the right of the origin, and the y-coordinate is -3, which means a vertical shift down 3 units. 

This point is located in Quadrant IV with a positive x-value and a negative y-value.

quadrant example

One quick note: not all points reside in a quadrant. For example, points of the form (0, y) reside on the y-axis and points of the form (x, 0) reside on the x-axis. 

So, with (2, -3), the x-coordinate is 2, which means a horizontal shift of 2 units to the right of the origin, and the y-coordinate is -3, which means a vertical shift down 3 units. This point is located in Quadrant IV with a positive x-value and a negative y-value.

Now you know what goes where—happy graphing! 

Catch up (or get ahead!) in math

Summertime and math might not seem like a perfect match, but now is the perfect time to break the typical school mold and make math fun! Get hands-on with an engaging challenge, math competition, or game. 

If math is not your child’s strong suit, now is also an excellent opportunity to get them caught up! Put a spin on this important subject with interesting math facts and apps (especially if your child isn’t the biggest math fan!) 

For additional support, Margo’s math expertise spans other key math topics bound to come up in algebra, geometry, and other subjects. Check out here step-by-step tutorials:

Or jump straight to our hub of math help, tips, and resources! Looking ahead to back-to-school season? iD Tech’s rockstar instructors offer 1-on-1 math tutoring, and lessons in subjects ranging from pre-algebra to calculus and statistics

Level up your child’s math skills today! 

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Virginia started with iD Tech at the University of Denver in 2015 and has loved every minute since then! A former teacher by trade, she has a master's in education and loves working to embolden the next generation through STEM. Outside the office, you can usually find her reading a good book, struggling on a yoga mat, or exploring the Rocky Mountains.