Analytic Geometry

The link between algebra and geometry was made possible by the development of a coordinate system which allowed geometric ideas, such as point and line, to be described in algebraic terms like real numbers and equations. In the system developed by Descartes, called the rectangular cartesian coordinate system, points on a geometric plane are associated with an ordered pair of real numbers known as coordinates. Each coordinate describes the location of a single point relative to a fixed point, the origin, which is created by the intersection of a horizontal and a vertical line known as the x-axis and y-axis respectively. The relationship between a point and its coordinates is called one-to-one since each point corresponds to only one set of coordinates.

The x and y axes divide the plane into four quadrants. The sign of the coordinates is either positive or negative depending in which quadrant the point is located. Starting in the upper right quadrant and working clockwise, a point in the first quadrant would have a positive value for the abscissa and the ordinate. A point in the fourth quadrant (lower right hand corner) would have negative values for each coordinate.

The notation P (x,y) describes a point P having coordinates x and y. The x value, called the abscissa, represents the horizontal distance of a point away from the origin. The y value, known as the ordinate, represents the vertical distance of a point away from the origin.