Distance Command

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Distance[ <Point>, <Object> ]
Yields the shortest distance between a point and an object.
Example:
Distance[(2, 1), x^2 + (y - 1)^2 = 1] yields 1
Note: The command works for points, segments, lines, conics, functions and implicit curves. For functions it uses a numerical algorithm which works better for polynomials.
Example: Let f be a function and A be a point. Distance[A, f] yields the distance between A and (x(A), f(x(A))).


Distance[ <Line>, <Line> ]
Yields the distance between two lines.
Example:
  • Distance[y = x + 3, y = x + 1] yields 1.41
  • Distance[y = 3x + 1, y = x + 1] yields 0
Note: The distance between intersecting lines is 0. Thus, this command is only interesting for parallel lines.
Note: See also Mode distance.svg Distance or Length tool .


Distance[ <Point>, <Point> ]
Yields the distance between the two points.
Example:
Distance[(2, 1, 2), (1, 3, 0)] yields 3
Distance[ <Line>, <Line> ]
Yields the distance between two lines.
Example:
Let a: X = (-4, 0, 0) + λ*(4, 3, 0) and b: X = (0, 0, 0) + λ*(0.8, 0.6, 0).
Distance[a, b] yields 2.4
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