Definition:Cartesian Plane/Ordered Pair

Identification of Point in Plane with Ordered Pair
Every point on the plane can be identified by means of an ordered pair of real coordinates $\tuple {x, y}$, as follows:

Identify one distinct point on the plane as the origin $O$.

Select a point $P$ on the plane different from $O$.

Let the distance from the origin to $P$ be defined as being $1$.

Draw an infinite straight line through $O$ and $P$ and call it the $x$-axis.

Draw an infinite straight line through $O$ perpendicular to $OP$ and call it the $y$-axis.

Now, let $Q$ be any point on the plane.

Draw two lines through $Q$, parallel to the $x$-axis and $y$-axis.

The plane is then conventionally oriented so that the $x$-axis is horizontal with $P$ being to the right of $O$.

Thus the $y$-axis is then a vertical line.

Thus the point $Q$ can be uniquely identified by the ordered pair $\tuple {x, y}$ as follows:

$y$ Coordinate
The point $P$ is identified with the coordinates $\tuple {1, 0}$.

Also known as
The ordered pair $\tuple {x, y}$ which determine the location of $P$ in the cartesian plane can be referred to as the rectangular coordinates or (commonly) just coordinates of $P$.