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Normal vector in red, line in green, point O shown in blue. The Hesse normal form named after Otto Hesse, is an equation used in analytic geometry, and describes a line in or a plane in Euclidean space or a hyperplane in higher dimensions. [1][2] It is primarily used for calculating distances (see point-plane distance and point-line distance).
Cartesian coordinate system with a circle of radius 2 centered at the origin marked in red. The equation of a circle is (x − a)2 + (y − b)2 = r2 where a and b are the coordinates of the center (a, b) and r is the radius. Cartesian coordinates are named for René Descartes, whose invention of them in the 17th century revolutionized ...
The distance from a point to a plane in three-dimensional Euclidean space [7] The distance between two lines in three-dimensional Euclidean space [8] The distance from a point to a curve can be used to define its parallel curve, another curve all of whose points have the same distance to the given curve. [9]
In mathematics, the abscissa (/ æbˈsɪs.ə /; plural abscissae or abscissas) and the ordinate are respectively the first and second coordinate of a point in a Cartesian coordinate system: -axis (vertical) coordinate. Usually these are the horizontal and vertical coordinates of a point in plane, the rectangular coordinate system.
In blue, the point (4, 210°). In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to the origin of a Cartesian coordinate system) is called the pole, and the ...
Distance from a point to a plane. 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 ...
In geometry, a Euclidean plane isometry is an isometry of the Euclidean plane, or more informally, a way of transforming the plane that preserves geometrical properties such as length. There are four types: translations, rotations, reflections, and glide reflections (see below § Classification ). The set of Euclidean plane isometries forms a ...
A rotation in the plane can be formed by composing a pair of reflections. First reflect a point P to its image P′ on the other side of line L1. Then reflect P′ to its image P′′ on the other side of line L2. If lines L1 and L2 make an angle θ with one another, then points P and P′′ will make an angle 2θ around point O, the ...