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In Euclidean space, the distance from a point to a plane is the distance between a given point and its orthogonal projection on the plane, the perpendicular distance to the nearest point on the plane.
It can be found starting with a change of variables that moves the origin to coincide with the given point then finding the point on the shifted plane a x + b y + c z = d {\displaystyle ax+by+cz=d} that is closest to the origin. The resulting point has Cartesian coordinates {\displaystyle } :
The distance between the origin and the point {\displaystyle } is x 2 + y 2 + z 2 {\displaystyle {\sqrt {x^{2}+y^{2}+z^{2}}}}.