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How to Graph Points on a Coordinate Plane

Cartesian coordinate plane

A coordinate plane is a two-dimensional plane with an x-axis (horizontal) and a y-axis (vertical). These axes intersect to form a perpendicular line that separates the coordinate plane into four quadrants.

How to Use a Coordinate Plane

You use coordinate planes for plotting points on graphs. Each quadrant is written in Roman numerals and has a different location within the plane. For example, the first quadrant (Quadrant I) lies to the right of the vertical axis and above the horizontal axis:

Coordinate plane with quadrants

Image credit: Desmos

When you're asked to graph points, you will be given ordered pairs written within parentheses. For example, if a point has an x-value of 1 and a y-value of -2 it would be written as (1, -2). The first number represents the x-coordinate, the point on the horizontal axis, and the second number represents the y-coordinate, the point on the vertical axis.

The quadrant that each point lies on depends on whether the coordinates of the point are negative or positive numbers. Here’s a breakdown of how each quadrant is classified:

Quadrant I: Positive x and y-values

Quadrant II: Positive y-values, negative x-values

Quadrant III: Negative x- and y-values

Quadrant IV: Positive x-values, negative y-values

Let's determine the quadrants of each given point, which lists the x-value first and the y-value second:

Point A: (3, 2)

Since this point has a positive x-value of 3 and a positive y-value of 2, it belongs in Quadrant I.

Point B: (-2, 2)

The y-value is positive but the x-value is negative, so this point will go in Quadrant II.

Point C: (-2, -1)

Both the x- and y-values are negative, so this point is located in Quadrant III.

Point D: (3, -1)

The x-value is positive but the y-value is negative, so this point goes in Quadrant IV.

Coordinate plane with values

Image credit: Desmos

When Do You Use a Coordinate Plane?

Any time you graph points on the negative or positive x or y axis, you are using a coordinate plane. When you know how to plot points and determine their corresponding quadrants, you can start graphing linear equations, exponential values, and more. Learning how to use a coordinate plane is one of the most useful and fundamental concepts in math.

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