In order to improve the mind, we ought less to learn than to contemplate.
-Rene Descartes, philosopher and mathematician (1596-1650)
René Descartes was the first to use a graph to provide a geometric interpretation of a mathematical equation. The Cartesian coordinate system is named after him. Cartesian coordinates (also known as rectangular coordinates) are linear and perpendicular to each other in two or three dimensions. The same unit of length is used for each dimension. Each coordinate of a point may lie anywhere in the interval (-∞, +∞).
By convention, the horizontal line is called the x-axis; it is positive to the right and negative to the left. The vertical line is called the y-axis, which is positive upward and negative downward. In three dimensions, the z-axis would be positive above the x-y plane and negative below. The intersection of these axes is called the origin. At the origin, the value of each coordinate is zero. The intersection of the axes divides the x-y plane into four regions called quadrants numbered counterclockwise from one to four. A point located on an axis is not in any quadrant.
9.1. Points
9.2. Distance
9.3. Equations in two variables
9.4. Symmetry
9.5. Solved problems