Difference between revisions of "Distance Command"
From GeoGebra Manual
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}} | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}} | ||
;Distance( <Point>, <Object> ): Yields the shortest distance between a point and an object. | ;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)))''.}} | ::{{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)))''.}} | ||
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<br> | <br> | ||
;Distance( <Line>, <Line> ): Yields the distance between two lines. | ;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 = x + 3, y = x + 1)</nowiki></code> yields ''1.41'' | ||
:*<code><nowiki>Distance(y = 3x + 1, y = x + 1)</nowiki></code> yields ''0''</div>}} | :*<code><nowiki>Distance(y = 3x + 1, y = x + 1)</nowiki></code> yields ''0''</div>}} | ||
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;Distance( <Point>, <Point> ) | ;Distance( <Point>, <Point> ) | ||
: 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( <Line>, <Line> ) | ;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 10:16, 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 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
