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  2. Line coordinates - Wikipedia

    en.wikipedia.org/wiki/Line_coordinates

    The coordinates depend on the presence of an origin and reference line on it. Then, given an arbitrary line its coordinates are found from the intersection with the reference line. The distance s from the origin to the intersection and the angle θ of inclination between the two lines are used:

  3. Line–line intersection - Wikipedia

    en.wikipedia.org/wiki/Lineline_intersection

    We can convert 2D points to homogeneous coordinates by defining them as (x, y, 1). Assume that we want to find intersection of two infinite lines in 2-dimensional space, defined as a 1 x + b 1 y + c 1 = 0 and a 2 x + b 2 y + c 2 = 0. We can represent these two lines in line coordinates as U 1 = (a 1, b 1, c 1) and U 2 = (a 2, b 2, c 2).

  4. Distance from a point to a line - Wikipedia

    en.wikipedia.org/.../Distance_from_a_point_to_a_line

    The equation of a line can be given in vector form: = + Here a is the position of a point on the line, and n is a unit vector in the direction of the line. Then as scalar t varies, x gives the locus of the line. The distance of an arbitrary point p to this line is given by

  5. Line (geometry) - Wikipedia

    en.wikipedia.org/wiki/Line_(geometry)

    a coordinate line, a linear coordinate dimension; In the context of determining parallelism in Euclidean geometry, a transversal is a line that intersects two other lines that may or not be parallel to each other. For more general algebraic curves, lines could also be: i-secant lines, meeting the curve in i points counted without multiplicity, or

  6. Intersection (geometry) - Wikipedia

    en.wikipedia.org/wiki/Intersection_(geometry)

    The intersection of a line and a plane in general position in three dimensions is a point. Commonly a line in space is represented parametrically ((), (), ()) and a plane by an equation + + =. Inserting the parameter representation into the equation yields the linear equation

  7. Coordinate system - Wikipedia

    en.wikipedia.org/wiki/Coordinate_system

    Given a coordinate system, if one of the coordinates of a point varies while the other coordinates are held constant, then the resulting curve is called a coordinate curve. If a coordinate curve is a straight line , it is called a coordinate line .

  8. Distance between two parallel lines - Wikipedia

    en.wikipedia.org/wiki/Distance_between_two...

    the distance between the two lines is the distance between the two intersection points of these lines with the perpendicular line y = − x / m . {\displaystyle y=-x/m\,.} This distance can be found by first solving the linear systems

  9. Rotation of axes in two dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotation_of_axes_in_two...

    A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system. [1] In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly.