How are the four quadrants arranged in a Cartesian coordinate plane?

The Cartesian coordinate system, named after the French mathematician and philosopher René Descartes, uses two perpendicular axes—the horizontal x-axis and the vertical y-axis—that intersect at the origin (0, 0). These axes divide the two-dimensional plane into four quadrants, which are typically labeled I through IV in a counterclockwise direction starting from the upper right.1

The quadrants are arranged based on the signs of the coordinates $(x,y)$ as follows:

| Quadrant | x-value | y-value |
| :--- | :--- | :--- |
| I | Positive | Positive |
| II | Negative | Positive |
| III | Negative | Negative |
| IV | Positive | Negative |

This system allows for the precise identification of any point on the plane by its distance from the origin along each axis.21