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 | + | ;Distance( <Point>, <Object> ): Yields the shortest distance between a point and an object. |
:{{example|1=<div><code><nowiki>Distance[(2, 1), x^2 + (y - 1)^2 = 1]</nowiki></code> yields ''1''</div>}} | :{{example|1=<div><code><nowiki>Distance[(2, 1), x^2 + (y - 1)^2 = 1]</nowiki></code> yields ''1''</div>}} | ||
: {{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. | ||
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}} | }} | ||
<br> | <br> | ||
| − | ;Distance | + | ;Distance( <Line>, <Line> ): Yields the distance between two lines. |
:{{example|1=<div> | :{{example|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'' | ||
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| − | ;Distance | + | ;Distance( <Point>, <Point> ) |
: Yields the distance between the two points. | : Yields the distance between the two points. | ||
:{{example|1=<div><code><nowiki>Distance[(2, 1, 2), (1, 3, 0)]</nowiki></code> yields ''3''</div>}} | :{{example|1=<div><code><nowiki>Distance[(2, 1, 2), (1, 3, 0)]</nowiki></code> yields ''3''</div>}} | ||
| − | ;Distance | + | ;Distance( <Line>, <Line> ) |
:Yields the distance between two lines. | :Yields the distance between two lines. | ||
:{{example|1=<div>Let ''a: X = (-4, 0, 0) + λ*(4, 3, 0)'' and ''b: X = (0, 0, 0) + λ*(0.8, 0.6, 0)''.<br><code><nowiki>Distance[a, b]</nowiki></code> yields ''2.4''</div>}} | :{{example|1=<div>Let ''a: X = (-4, 0, 0) + λ*(4, 3, 0)'' and ''b: X = (0, 0, 0) + λ*(0.8, 0.6, 0)''.<br><code><nowiki>Distance[a, b]</nowiki></code> yields ''2.4''</div>}} | ||
Revision as of 17:16, 7 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.
- Example:
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
