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How are three-dimensional Cartesian coordinates written?

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Diagram showing a double cone intersected by planes at different angles, producing the conic sections: a horizontal plane creates a circle, a tilted plane creates an ellipse, a plane parallel to the cone's side forms a parabola, and a steep plane produces a hyperbola. Each section is labeled, with the axis and apex of the cone indicated. — analytic geometry The conic sections result from intersecting a plane with a double cone, as shown in the figure. There are three distinct families of conic sections: the ellipse (including the circle), the parabola (with one branch), and the hyperbola (with two branches).

In analytic geometry, three-dimensional Cartesian coordinates are written as an ordered triple of numbers in the form:

(x, y, z)1

In this system, the position of a point is defined by its distance from the origin along three mutually perpendicular axes. The x and y values represent the point's location relative to the horizontal and vertical axes, while the z-axis represents the third dimension, intersecting the origin and remaining perpendicular to the plane formed by the x- and y-axes.1