By Victoria Smoothens Updated Aug 30, 2022
The x‑axis and y‑axis are the backbone of the Cartesian, or rectangular, coordinate system. In this framework, every point is located by its distance from two perpendicular lines that intersect at a single spot.
René Descartes, a French philosopher and mathematician, pioneered this system in 1637. In his seminal work, Discourse on the Method of Reasoning Well and Seeking Truth in the Sciences, he introduced the section titled La Géométrie—the first formal marriage of geometry and algebra.
The system consists of two number lines: a horizontal x‑axis and a vertical y‑axis. Their perpendicular intersection creates four quadrants and establishes the origin, denoted (0, 0). Distances from this origin along each axis define the coordinates of any point.
Because both axes cross at zero, the intersection point is expressed as (0, 0). This coordinate serves as the reference for all other points in the plane.
• Quadrant I (upper right): positive x and y, e.g., (1, 1)
• Quadrant II (upper left): negative x, positive y, e.g., (−1, 1)
• Quadrant III (lower left): negative x and y, e.g., (−1, −1)
• Quadrant IV (lower right): positive x, negative y, e.g., (1, −1)
