Coordinate System in Geometry: Definition & Types

Instructor: David Karsner
Coordinate systems use 1-dimensional, 2-dimensional and 3-dimensional spaces and coordinates to define points. The ''xy'' coordinate grid is the most common of these systems, which you can learn how to use in this lesson.

What is a Coordinate System?

Imagine that you are in New York City on a vacation and have picked up a sightseeing map. In looking for location of the Statue of Liberty, you see it has a designation of A3, or the meeting place of column A and row 3. Whether you realize it or not, you've just used a coordinate system, which typically assigns numbers, or coordinates, to a point in space. Coordinate systems use one, two, or three coordinates representing 1-dimensional, 2-dimensional or 3-dimensional spaces.

One-Dimensional Coordinate Systems

A 1-dimensional coordinate system, also known as a number line, uses one coordinate to tell how far away from zero it is located. You can find an example of a 1-dimensional coordinate system below.

Number Line
number line

Two-Dimensional Coordinate Systems

In a 2-dimensional coordinate system, you use two values to give the location. The most commonly used coordinate system is called the xy coordinate grid, which consists of two 1-dimensional number lines that intersect perpendicular to each other at the 0 coordinate. The horizontal number line is called the x-axis, while the vertical number line is known as the y-axis. The point at which both lines intersect is called the origin, which uses the coordinates of (0,0).

All points within a 2-dimensional space are given by an ordered pair (x,y). The first number, or x, tells us how far to move from the origin along the x-axis, either left or right. Positive numbers move right, while negative numbers move left. The second number, or y, tells us how far to move along the y-axis, either up or down. Positive numbers move up, while negative numbers move down.

The x-axis and y-axis divide the coordinate plane into four sections known as quadrants, which are typically indicated by Roman numerals. In the upper-right, or quadrant I, both the x and y values are positive. Quadrant II is located in the upper-left corner; here, the x values are negative, while the y values are positive. In the bottom-left, or quadrant III, both the x and y values are negative. Quadrant IV is located in the bottom-right corner, where the x values are positive, and the y values are negative.

XY coordinate grid
XY coordinate grid

Take a look at the above image: do you see four points labeled A, B, C and D? Now, beginning at the origin, try to find point B(-3, 2). As the first number is -3, you'll move three place to the left. As the second number is 2, you'll move two places up to point B. You can try the exercise again using points, A, C and D.

There are other 2-dimensional coordinate systems that are not as common as the xy coordinate system. These include the polar coordinate system, where the x-axis and y-axis represent the distance from a point and the degree of rotation. In the complex numbers system, one axis represents the real part of a complex number, while the other axis represents the imaginary part of a complex number.

To unlock this lesson you must be a Study.com Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create An Account
Support