A coordinate system is a reference framework used to describe the positions of objects like points, lines, and surfaces in a space. A fixed point called the origin is used as a reference in the coordinate system. The most common types of coordinate systems are one-, two-, or three-dimensional.

Number Line

A number line is a one-dimensional coordinate system. The origin represents the number $0.$ Negative numbers are placed along the line on the left-hand side of $0,$ while positive numbers are placed on the right-hand side of $0.$ Any real number can be graphed as a unique point on the number line.

Coordinate Plane

A coordinate plane is a two-dimensional coordinate system. It is a grid that results from intersecting a vertical number line with a horizontal number line at their zero points. The horizontal number line is usually named the $x\text{-}$axis and the vertical number line is usually the $y\text{-}$axis.

The positive numbers on the $y\text{-}$axis are above zero and the negative ones are below zero. The origin is where the lines intersect, which is the point $(0,0).$ Every point on a coordinate plane is plotted according to its $x\text{-}$ and $y\text{-}$coordinates.

Three Dimensional Coordinate System

In a three-dimensional coordinate system, three axes intersect. Each axis is perpendicular to the other two axes. These axes are commonly labeled as the $x\text{-}$axis, the $y\text{-}$axis, and the $z\text{-}$axis. The origin of this system is the point $(0,0,0)$ where the three axes intersect.

Note that in this case, the $x\text{-}$axis goes from front to back, the $y\text{-}$axis from left to right, and the $z\text{-}$axis from bottom to top. Any point in a three-dimensional system requires three coordinates called an ordered triple $(x,y,z).$