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How does the Cartesian coordinate system represent a point with an ordered pair?

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Map of the Greco-Roman world highlighting the birthplaces of notable ancient mathematicians, marked with the pi symbol and labeled with their names. Cities such as Athens, Alexandria, Syracuse, and Miletus are shown around the Mediterranean, with modern country boundaries outlined. An inset provides detail for the region of Greece and western Anatolia. — algebra This map spans a millennium of prominent Greco-Roman mathematicians, from Thales of Miletus (c. 600 bce) to Hypatia of Alexandria (c. 400 ce).

In the Cartesian coordinate system, a point in a two-dimensional plane is represented by an ordered pair of numbers, typically denoted as $(x, y)$ .12

This system utilizes two perpendicular axes that intersect at a reference point called the origin, which is designated as $(0, 0)$ . The representation works as follows:31

The x-coordinate: The first number in the pair represents the point's horizontal distance from the origin along the x-axis.14
The y-coordinate: The second number in the pair represents the point's vertical distance from the origin along the y-axis.14

By identifying these two distances, the ordered pair provides a unique address for any point within the plane. This method of pairing space with numbers is fundamental to analytic geometry, allowing for the algebraic solution of geometric problems and the graphing of functions.12