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Coordinate Plane – Definition, Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Coordinate PlaneCoordinate Plane – Definition, ExamplesTable of ContentsCoordinate Plane Definition of Coordinate Plane

A coordinate plane is a two-dimensional plane created by the intersection of two perpendicular number lines. The horizontal number line is called the x-axis, and the vertical number line is called the y-axis. These axes meet at a point called the origin, which has coordinates (0, 0). The coordinate plane allows us to locate points using ordered pairs (x, y), where x shows the horizontal position and y shows the vertical position.

The coordinate plane is divided into four regions called quadrants, numbered using Roman numerals I, II, III, and IV. In Quadrant I, both x and y values are positive. In Quadrant II, x is negative and y is positive. In Quadrant III, both x and y are negative. In Quadrant IV, x is positive and y is negative. Points on the x-axis have y = 0 and are written as (x, 0), while points on the y-axis have x = 0 and are written as (0, y). Historically, this system is called the Cartesian coordinate system after its inventor, French mathematician René Descartes.

Examples of Coordinate Plane Example 1: Finding Quadrants of Points Problem:

In which quadrants of the coordinate plane do the following points lie?

A (–2, 4) B (2, 3) C (4, –2) D (6, 1) Step-by-step solution:

Step 1, Find the quadrant for point A (–2, 4). Since x is negative (-2) and y is positive (4), point A is in the second quadrant.

Step 2, Find the quadrant for point B (2, 3). Since x is positive (2) and y is positive (3), point B is in the first quadrant.

Step 3, Find the quadrant for point C (4, –2). Since x is positive (4) and y is negative (-2), point C is in the fourth quadrant.

Step 4, Find the quadrant for point D (6, 1). Since x is positive (6) and y is positive (1), point D is in the first quadrant.

Finding Quadrants of Points

Example 2: Identifying Points on an Axis Problem:

Which of the following points lie on the y-axis? Explain your answer.

(i) (0, 3) (ii) (5, 0) (iii) (–2, 0) (iv) (0, –2) (v) (–1, 3)

Identifying Points on an Axis

Step-by-step solution:

Step 1, Recall what makes a point lie on the y-axis. A point lies on the y-axis when its x-coordinate equals zero.

Step 2, Check each point one by one:

For point (0, 3): The x-coordinate is 0, so this point lies on the y-axis. For point (5, 0): The x-coordinate is 5, not 0, so this point doesn't lie on the y-axis. For point (–2, 0): The x-coordinate is -2, not 0, so this point doesn't lie on the y-axis. For point (0, –2): The x-coordinate is 0, so this point lies on the y-axis. For point (–1, 3): The x-coordinate is -1, not 0, so this point doesn't lie on the y-axis.

Step 3, Make a final list. Points (i) (0, 3) and (iv) (0, –2) lie on the y-axis.

Example 3: Moving Points on the Coordinate Plane Problem:

You are at (−4, 3). Move 5 units right and 2 units up. Write the coordinates of point where you reach.

Step-by-step solution: Step 1, Start at the initial point (−4, 3).

Moving Points on the Coordinate Plane

Step 2, Moving 5 units right means adding 5 to the x-coordinate.

New x-coordinate = −4 + 5 = 1

Step 3, Moving 2 units up means adding 2 to the y-coordinate.

New y-coordinate = 3 + 2 = 5

Step 4, Put together the new coordinates. The new point is at (1, 5).

Moving Points on the Coordinate Plane

Comments(6)AArtTutorJillNovember 6, 2025I've used this coordinate plane def for my students. It's clear & helped them grasp plotting points. Thanks for the great resource!

MCMs. CarterSeptember 17, 2025I used this coordinate plane definition and examples to help my son with his homework, and it made a big difference! The clear explanation of quadrants and plotting points really clicked for him.

NNatureLover87September 10, 2025This definition of the coordinate plane was super clear! I used the examples to help my kids practice plotting points, and they finally got it. Great resource for visual learners!

MCMs. CarterAugust 27, 2025I used the Coordinate Plane definition and examples to help my 6th grader with homework, and it really clicked for them! The quadrant explanations were super clear. Great resource for visual learners!

MCMs. CarterAugust 19, 2025I used the coordinate plane explanation with my 5th grader, and it clicked instantly! The examples were super helpful for plotting points and understanding quadrants. Great resource for visual learners!

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