Definition4.1.8Cartesian Coordinate System

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed (positive/negative) distances to the point from two fixed perpendicular directed lines, measured in the same unit of length. Those two reference lines are called the horizontal axis and vertical axis, and the point where they meet is the origin. The horizontal and vertical axes are often called the \(x\)-axis and \(y\)-axis. (Visit for more.)

The plane based on the \(x\)-axis and \(y\)-axis is called a coordinate plane. The ordered pair used to locate a point is called the point's coordinates, which consists of an \(x\)-coordinate and a \(y\)-coordinate. For example, for the point \((1,2)\text{,}\) its \(x\)-coordinate is \(1\text{,}\) and its \(y\)-coordinate is \(2\text{.}\) The origin has coordinates \((0,0)\text{.}\)

A Cartesian coordinate system is divided into four quadrants, as shown in FigureĀ 4.1.9. The quadrants are traditionally labeled with Roman numerals.

a Cartesian grid with Quadrant I marked in the top right section, Quadrant II marked in the top left section, Quadrant III marked in the bottom left section, Quadrant IV marked in the bottom right section.
Figure4.1.9A Cartesian grid with four quadrants marked