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.

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