Definition of Coordinate Plane
Definition
The coordinate plane is created by drawing two perpendicular lines that intersect at $0$ in an orthogonal manner. These lines are referred to as axes. The horizontal line is called the $x$ axis, and the vertical line is called the $y$ axis.
A line drawn orthogonally to the $x$ axis at the real number $a$ on the $x$ axis, and a line drawn orthogonally to the $y$ axis at the real number $b$ on the $y$ axis, intersect at a point called point $(a, b)$. Specifically, point $(0, 0)$ is called the origin.
In point $p=(a, b)$, $a$ is called the $x$ coordinate of $p$, and $b$ is called the $y$ coordinate of $p$.
- The set of points where the $x$ coordinate is positive, and the $y$ coordinate is positive, is called the Quadrant $\mathrm{I}$.
- The set of points where the $x$ coordinate is negative, and the $y$ coordinate is positive, is called the Quadrant $\mathrm{II}$.
- The set of points where the $x$ coordinate is negative, and the $y$ coordinate is negative, is called the Quadrant $\mathrm{III}$.
- The set of points where the $x$ coordinate is positive, and the $y$ coordinate is negative, is called the Quadrant $\mathrm{IV}$.
Explanation
Named after Descartes, who is credited with its creation, this (two-dimensional) system is also referred to as the Cartesian coordinate system. By adding one more axis, it becomes a coordinate space.
The order of the quadrants starts where both coordinates are positive and proceeds in a counterclockwise direction (the standard direction in mathematics is always counterclockwise).