Geometry/Period ___
Compound Loci notes
Name: _______________________
Date: ________________________
How do we solve problems involving Compound Loci?
A compound locus problem involves two, or possibly more, locus conditions occurring
at the same time. The different conditions in a compound locus problem are generally
separated by the word "AND" or the words "AND ALSO".
Steps for solving a compound locus problem
1. Prepare each condition separately on the SAME DIAGRAM. You many need to
create the diagram yourself!
2. After the two conditions are drawn, count the number of points where the two loci
conditions intersect.
3. The intersection is the point(s) that satisfy both conditions.
Example:
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.
1. Maria’s backyard has two trees that are 40 feet apart, as shown in the
accompanying diagram. She wants to place lampposts so that the posts are 30 feet
from both of the trees. Draw a sketch to show where the lampposts could be
placed in relation to the trees. How many locations for the lampposts are possible?
2. The distance between parallel lines and m is 12 units. Point A is on line .
How many points are equidistant from lines and m and 8 units from point A.
3. In the diagram below, town C lies on straight road p. Sketch the points that are 6
miles from town C. Then sketch the points that are 3 miles from road p. How
many points satisfy both conditions?
4. In the accompanying diagram, point P lies 3 centimeters from line . How many
points are both 2 centimeters from line and 1 centimeter from point P?