Locus

Pronunciation: /ˈloʊ kəs/ ?

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Manipulative 1: Line as a locus of points. Created with GeoGebra.

A locus is a set of points that satisfy a condition.[1] The points may be continuous. For example, a line is the locus of all points equidistant from two points.

Click on the blue points in manipulative 1 and drag them to change the figure. Points A and B are the points on which the line is defined. Dragging point C draws the line composed of points equidistant from points A and B.

Manipulative 2 is the locus of all points equidistant from a center. Click on the blue point in manipulative 2 and drag it to see the locus.

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Manipulative 2: Locus of points equidistant from a center. Created with GeoGebra.

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Manipulative 3: Locus of points equidistant from a point and a line. Created with GeoGebra.

Manipulative 3 lets you construct the locus of points equidistant from a point and a line. Click on the blue point on the directrix and drag it to construct the locus. What figure is being constructed?

Compound Locus

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Manipulative 5: Compound locus. Created with GeoGebra.

A compound locus is a locus with more than one condition. The points included in the locus must meet all of the conditions.

Manipulative 5 illustrates a locus of all points equidistant from A and B that lie within the disk centered at A with a radius AB. Note: The GeoGebra application will draw some points outside of the disk. This is due to a flaw in GeoGebra.

References

  1. locus. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=locus&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  2. Hilbert, David. The Foundations of Geometry, pg 28. Townsend, E. J., Ph. D.. The Open Court Publishing Company, 1950. (Accessed: 2009-12-21). http://www.gutenberg.org/files/17384/17384-pdf.pdf.

Cite this article as:


Locus. 2009-12-21. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/l/locus.html.

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Revision History


2009-12-21: Added "References" (McAdams, David.)
2008-12-12: Added compound locus (McAdams, David.)
2008-12-11: Initial version (McAdams, David.)

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