What 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?
Cartesian coordinate system Cartesian coordinate system A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a set of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length. Each reference line is called a "coordinate axis" or just "axis" (plural "axes") of the system, and the point where they meet is its "origin", at ordered pair . The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from
Distance from a point to a plane We define formula_8, formula_9, formula_10, and formula_11, to obtain formula_1 as the plane expressed in terms of the transformed variables. Now the problem has become one of finding the nearest point on this plane to the origin, and its distance from the origin. The point on the plane in terms of the original coordinates can be found from this point using the above relationships between formula_13 and formula_14, between formula_15 and formula_16, and between formula_17 and formula_18; the distance in terms of the original coordinates is the same as the distance in terms of the revised coordinates. The formula for