Cartesian coordinate system

In mathematics and geometry, the Cartesian coordinate system is a coordinate system used to give the location of points on a plane by using two numbers for each point. It is also called the rectangular coordinate system. The numbers are usually called the ${\displaystyle x}$ coordinate and the ${\displaystyle y}$ coordinate. To find the coordinates of a point, two perpendicular lines, called axes (singular: axis), are drawn. The point where the axes meet is the coordinate origin, written (0,0). The ${\displaystyle x}$ coordinate gives the position of a point measured along the ${\displaystyle x}$ axis, and the ${\displaystyle y}$ coordinate gives the position along the ${\displaystyle y}$ axis. Cartesian coordinates can be used in three dimensions (3D), by adding a third number, the ${\displaystyle z}$ coordinate. In four dimensions (4D), a fourth number, the ${\displaystyle w}$ coordinate, is added. Each coordinate represents a dimension of space.
Using the Cartesian coordinate system, many shapes, like straight lines and parabolas can be described by using algebraic equations. The results of the equations can be seen by plotting (drawing) a point for each solution to the equations. For example, the ${\displaystyle x}$ axis is described by the equation ${\displaystyle y=0}$. A circle having radius ${\displaystyle r}$ and centered at the origin can be described with the equation ${\displaystyle x^{2}+y^{2}=r^{2}}$ (see Figure 2).
Cartesian coordinate system with the circle of radius 2 centered at the origin marked in red. The equation of the circle is ${\displaystyle x^{2}+y^{2}=4}$.