Ordinates

Ordinates is a term used in Cartesian coordinate systems to denote the coordinates along a given axis, most commonly the vertical axis. In two-dimensional analytic geometry, the ordinate of a point is its second coordinate y in the ordered pair (x, y). The first coordinate x is called the abscissa. The ordinate measures the point’s vertical position relative to the origin and can be positive or negative.

In three-dimensional space, a point is described by (x, y, z). Here y and z can be thought of as ordinates with respect to the x-axis, or more generally as the coordinate components corresponding to their respective axes. In many contexts, any coordinate value may be referred to as an ordinate of the point with respect to the axis used for measurement.

In functions, the ordinate is the dependent variable: for a graph y = f(x), the ordinate is the function value at a given abscissa x. Thus as x varies, the ordinate traces the curve.

Beyond pure mathematics, ordinates appear in surveying and cartography to describe measured distances along a given direction, or the components of a point’s location in a grid. The terminology can vary by discipline; some writers reserve “ordinate” for the y-value, while others use it more broadly to mean any coordinate component.