Distance Command

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 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