# 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}} |

− | {{command|geometry}} | + | ;Distance( <Point>, <Object> ): Yields the shortest distance between a point and an object. |

− | ; Distance | + | :{{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. | |

− | ; Distance | + | ::{{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)))''.}} |

− | : {{Note| The distance between intersecting lines is 0. Thus, this command is only interesting for parallel lines.}} | + | }} |

− | + | <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 .}} | ||

+ | |||

+ | |||

+ | |||

+ | ;Distance( <Point>, <Point> ) | ||

+ | : Yields the distance between the two points. | ||

+ | :{{example|1=<code><nowiki>Distance((2, 1, 2), (1, 3, 0))</nowiki></code> yields ''3''}} | ||

+ | ;Distance( <Line>, <Line> ) | ||

+ | :Yields the distance between two lines. | ||

+ | :{{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''}} |

## Latest 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*1.41*`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*