A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis of the system.
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The cartesian coordinates are plotted on the cartesian plane
You do not have 3 coordinates in the Cartesian plane. The Cartesian plane is a plane and is therefore 2 dimensional. In 2 dimensional space you require only 2 coordinates. 3 coordinates are required to locate a point in 3-dimensional space but then it cannot be a Cartesian PLANE.
The x coordinates are horizontal whereas the y coordinates are vertical on the Cartesian plane.
If the polar coordinates of a point P are (r,a) then the rectangular coordinates of P are x = rcos(a) and y = rsin(a).
Cartesian coordinates are plotted on the Cartesian plane which consist of a horizontal x axis number line and a vertical y axis number line whereas both axes are perpendicular to each other and meet at right angles at the point of origin whose coordinates are at (0, 0)