Locus

Pronunciation: /ˈloʊ.kəs/ Explain

Click on points A and B and drag them to change the line being drawn. Click on point C and drag it to draw the line. Click the reset button to erase all drawn points.

This method of drawing a line uses the fact that a line can be determined as all points equidistant from two points.
Manipulative 1 - Line as Locus Created with GeoGebra.

A locus is a set of points that satisfy a condition.[2] 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.

Click on point A and distance and drag them to change the circle being drawn. Click on point B and drag it to draw the line. Click the reset button to erase all drawn points.

This method of drawing a circle uses the fact that a circle is all points equidistant from two points.
Manipulative 2 - Circle as Locus Created with GeoGebra.

Click on the blue points and drag them to change the figure. Click on the red point and drag it to trace the parabola. Click on the reset button to clear previous traces.

How can you arrange the line and point so that the parabola degenerates into a line?
Manipulative 3 - Parabola as a Locus of Points Created with GeoGebra.

Manipulative 3 lets you construct the locus of points equidistant from a point and a line.

Compound Locus

Click on the blue points and drag them to change the figure.

This locus of points is all points on the disk that are equidistant from the two points.
Manipulative 4 - 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 4 illustrates a locus of all points equidistant from A and B that lie within the disk centered at A with a radius AB.

References

  1. McAdams, David E.. All Math Words Dictionary, locus. 2nd Classroom edition 20150108-4799968. pg 110. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. Hilbert, David. The Foundations of Geometry. pg 28. Translated by Townsend, E. J., Ph. D.. The Open Court Publishing Company. 1950. Last Accessed 8/31/2018. http://www.gutenberg.org/files/17384/17384-pdf.pdf. Buy the book

Cite this article as:

 McAdams, David E. Locus. 4/24/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/l/locus.html.

Image Credits

Revision History

4/24/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
8/31/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
12/21/2009: Added "References". (McAdams, David E.)
12/12/2008: Added compound locus. (McAdams, David E.)
12/11/2008: Initial version. (McAdams, David E.)

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