March 7, 2012 , Aim: How do we find Compound Loci?

Compound Loci:
- Involves two or more, locus conditions occurring at the same time.
-The different conditions in a compound locus problem are separated by the word "AND" or the words "AND ALSO"


Examples:

Consider:  A treasure is buried in your backyard.  The picture below shows your backyard which contains a stump, a teepee, and a tree.  The teepee is 8 feet from the stump and 18 feet from the tree.  The treasure is equidistant from the teepee and the tree AND ALSO 6 feet from the stump.  Locate all possible points of the buried treasure.

Description:

The red line represents the locus which is equidistant from the teepee and the tree (the perpendicular bisector of the segment).  The blue circle represents the locus which is 6 feet from the stump.  These two loci intersect in two locations.  The treasure could be buried at either "X" location.



http://www.regentsprep.org/Regents/math/geometry/GL3/LocusCom.htm

Questions:

1.

What is the number of points in a plane two units from a given line and three units from a given point on the line? Explanation

Choose:  1  2   3 4

2.

Parallel lines r and s are 8 meters apart, and A is a point on line s.  How many points are equidistant from r and s and also 4 meters from A?  Answer

Choose:  0  1 2 3

http://www.regentsprep.org/Regents/math/geometry/GL3/PracLocC.htm