Ingeometry, theperpendicular distance between two objects is thedistance from one to the other, measured along aline that isperpendicular to one or both.

Thedistance from a point to a line is the distance to the nearestpoint on that line. That is the point at which asegment from it to the given point is perpendicular to the line.

Likewise, the distance from a point to acurve is measured by a line segment that is perpendicular to atangent line to the curve at the nearest point on the curve.

Thedistance from a point to a plane is measured as the length from the point along a segment that is perpendicular to the plane, meaning that it is perpendicular to all lines in the plane that pass through the nearest point in the plane to the given point.

Other instances include:

• Point on plane closest to origin, for the perpendicular distance from the origin to a plane in three-dimensional space
• Nearest distance between skew lines, for the perpendicular distance between two non-parallel lines in three-dimensional space

Perpendicular regression fits a line to data points by minimizing the sum of squared perpendicular distances from the data points to the line.Othergeometric curve fitting methods using perpendicular distance to measure the quality of a fit exist, as intotal least squares.

The concept of perpendicular distance may be generalized to

• orthogonal distance, between more abstract non-geometricorthogonal objects, as inlinear algebra (e.g.,principal components analysis);
• normal distance, involving asurface normal, between an arbitrary point and itsfoot on the surface. It can be used forsurface fitting and for definingoffset surfaces.

• Distance between sets
• Hypercycle (geometry)
• Moment of inertia
• Signed distance

• Orthogonality
• Distance

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