Summary:

• Each point of the plane has two coordinates. A Cartesian coordinate system in two dimensions (also called a rectangular coordinate system) is commonly defined by two axes, at right angles to each other, forming a plane (an xy-plane). The horizontal axis is labeled usually x, and the vertical axis is usually labeled y. Coordinates of the type described here are called Cartesian coordinates (after René Descartes, 1596 - 1650, who recognized the importance of coordinate systems for modern mathematics and changed his name, as was fashionable in his time, to the Latin form Cartesius) or rectangular coordinates (since the two axes are at a right angle, relative to one another).
  • Coordinate systems - Drawing plane
       
• The two axes, together with their orientations (the arrows) form a (Cartesian or rectangular) coordinate system.
  • Coordinate systems - Axes
  • Coordinate systems - Points
  • Coordinate systems - Examples
       
• In addition to the Cartesian coordinate systems, there are also polar coordinate systems. Polar coordinate system is defined by the length of the line denoted by r, and the orientation of the line denoted by its angle, q, with respect to the x-axis.
  • Polar coordinate systems in the plane