Difference between revisions of "Distance Command"

Latest revision as of 18:06, 5 January 2023

Distance( <Point>, <Object> )

Yields the shortest distance between a point and an object.

Examples:

Distance((2, 1), x^2 + (y - 1)^2 = 1) yields 1
Distance((2, 1, 2), (1, 3, 0)) yields 3
Let f be a function and A be a point. Distance(A, f) yields the distance between A and (x(A), f(x(A))).

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.

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
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

Note: The distance between intersecting lines is 0. Thus, this command is only interesting for parallel lines.

Distance( <Plane>, <Plane> ): Yields the distance between the two planes.; Example: Let eq1: x + y 2x = 1 and eq2: 2x + 2y +4z = -2. Distance(eq1, eq2) yields 0.82

Note: The distance between intersecting planes is 0. Thus, this command is only meaningful for parallel planes.

Note: See also

Distance or Length tool .

@@ Line 1: / Line 1: @@
-<noinclude>{{Manual Page|version=4.2}}</noinclude>
+<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[Point A, Object O]: Yields the (shortest) distance between points ''A'' and the Object. Works for Points, Segments, Lines, Conics and Implicit Curves. When ''f'' is a function, <code>Distance[A,f]</code> returns distance between ''A'' and ''(x(A),f(x(A)))''.
+:{{examples|1=<div>
-: {{Note| In GeoGebra 3.2  '''Distance[Point A, Segment]''' gave the distance to the segment extended to an infinite line. From GeoGebra 4.0 it gives the distance to the Segment itself. }}
+:*<code><nowiki> Distance((2, 1), x^2 + (y - 1)^2 = 1)</nowiki></code> yields ''1''
-; Distance[Line g, Line h]: Yields the distance between the parallel lines ''g'' and ''h''.
+:*<code><nowiki>Distance((2, 1, 2), (1, 3, 0))</nowiki> </code> yields ''3''
-: {{Note| The distance between intersecting lines is 0. Thus, this command is only interesting for parallel lines.}}
+:*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| See also [[Image:Tool Distance.gif]] [[Distance or Length Tool|Distance or Length]] tool .}}
+</div>}}
-{{betamanual|version=5.0|
+: {{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=From GeoGebra 5, this command will work with 3D objects as well}}
+<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''
+:* 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''</div>}}
+: {{Note| 1=The distance between intersecting lines is ''0''. Thus, this command is only interesting for parallel lines.}}
+<br>
+;Distance( <Plane>, <Plane> )
+: Yields the distance between the two planes.
+:{{example|1=Let ''eq1: x + y 2x = 1'' and ''eq2: 2x + 2y +4z = -2''.  <code><nowiki>Distance(eq1, eq2)</nowiki></code> yields ''0.82''}}
+: {{Note| 1=The distance between intersecting planes is 0. Thus, this command is only meaningful for parallel planes.}}
+<br>
+{{Note| 1=See also [[File:Mode distance.svg|link=|20px]] [[Distance or Length Tool|Distance or Length]] tool .}}

Difference between revisions of "Distance Command"

Latest revision as of 18:06, 5 January 2023

Distance

Command Categories (All commands)