Margo, math expert and Operations extraordinaire, is glad you asked! Quadrants will pop up on graphs 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.
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.
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!
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