Difference between revisions of "Distance Command"
From GeoGebra Manual
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− | <noinclude>{{Manual Page|version= | + | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}} |
− | ;Distance | + | ;Distance( <Point>, <Object> ): Yields the shortest distance between a point and an object. |
− | :{{example|1= | + | :{{example|1=<code><nowiki>Distance((2, 1), x^2 + (y - 1)^2 = 1)</nowiki></code> yields ''1''}} |
− | : {{Note| 1=The command works for points, segments, lines, conics, functions and implicit curves. For functions it uses a numerical algorithm which works better for polynomials. }} | + | : {{Note| 1=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. <code><nowiki>Distance(A, f)</nowiki></code> yields the distance between ''A'' and ''(x(A), f(x(A)))''.}} | ||
+ | }} | ||
+ | <br> | ||
+ | ;Distance( <Line>, <Line> ): Yields the distance between two lines. | ||
+ | :{{examples|1=<div> | ||
+ | :*<code><nowiki>Distance(y = x + 3, y = x + 1)</nowiki></code> yields ''1.41'' | ||
+ | :*<code><nowiki>Distance(y = 3x + 1, y = x + 1)</nowiki></code> yields ''0''</div>}} | ||
+ | : {{Note| 1=The distance between intersecting lines is ''0''. Thus, this command is only interesting for parallel lines.}} | ||
− | + | {{Note| 1=See also [[File:Mode distance.svg|link=|20px]] [[Distance or Length Tool|Distance or Length]] tool .}} | |
− | |||
− | : | ||
− | |||
− | |||
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− | + | ;Distance( <Point>, <Point> ) | |
− | ;Distance | ||
: Yields the distance between the two points. | : Yields the distance between the two points. | ||
− | :{{example|1= | + | :{{example|1=<code><nowiki>Distance((2, 1, 2), (1, 3, 0))</nowiki></code> yields ''3''}} |
− | ;Distance | + | ;Distance( <Line>, <Line> ) |
:Yields the distance between two lines. | :Yields the distance between two lines. | ||
− | :{{example|1= | + | :{{example|1=Let ''a: X = (-4, 0, 0) + λ*(4, 3, 0)'' and ''b: X = (0, 0, 0) + λ*(0.8, 0.6, 0)''. <code><nowiki>Distance(a, b)</nowiki></code> yields ''2.4''}} |
Revision as of 09:16, 11 October 2017
- 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.
- Examples:
Distance(y = x + 3, y = x + 1)
yields 1.41Distance(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