Cartesian coordinate system
![Illustration of a Cartesian coordinate plane. Four points are marked and labeled with their coordinates: (2,3) in green, (−3,1) in red, (−1.5,−2.5) in blue, and the origin (0,0) in purple.](/Images/godic/202502/06/Cartesian-coordinate-system.svg3554.png")
![Cartesian coordinate system with a circle of radius 2 centered at the origin marked in red. The equation of a circle is (x − a)2 + (y − b)2 = r2 where a and b are the coordinates of the center (a, b) and r is the radius.](/Images/godic/202502/06/Cartesian-coordinate-system-with-circle.svg3554.png")
![A three dimensional Cartesian coordinate system, with origin O and axis lines X, Y and Z, oriented as shown by the arrows. The tick marks on the axes are one length unit apart. The black dot shows the point with coordinates x = 2, y = 3, and z = 4, or (2,3,4).](/Images/godic/202502/06/Coord_system_CA_0.svg3554.png")
![The coordinate surfaces of the Cartesian coordinates (x, y, z). The z-axis is vertical and the x-axis is highlighted in green. Thus, the red plane shows the points with x = 1, the blue plane shows the points with z = 1, and the yellow plane shows the points with y = −1. The three surfaces intersect at the point P (shown as a black sphere) with the Cartesian coordinates (1, −1, 1).](/Images/godic/202502/06/Cartesian_coordinate_surfaces3554.png")
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 distances to the point from two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin, usually at ordered pair (0, 0). The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.