Difference between revisions of "Distance Command"
From GeoGebra Manual
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:* 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>}} | :* 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.}} | : {{Note| 1=The distance between intersecting lines is ''0''. Thus, this command is only interesting for parallel lines.}} | ||
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;Distance( <Plane>, <Plane> ) | ;Distance( <Plane>, <Plane> ) | ||
: Yields the distance between the two planes. | : 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''}} | :{{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.}} | : {{Note| 1=The distance between intersecting planes is 0. Thus, this command is only meaningful for parallel planes.}} | ||
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| + | {{Note| 1=See also [[File:Mode distance.svg|link=|20px]] [[Distance or Length Tool|Distance or Length]] tool .}} | ||
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 1Distance((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 1.41Distance(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 .
Distance or Length tool .
