Project AMP
Dr. Antonio R. Quesada – Director, Project AMP
Compound Locus
Lesson Summary:
This lesson poses a real-world problem for students to apply the idea of compound locus.
Students will work with the idea of equidistant from a point and from a line.
Key Words:
locus
Background knowledge:
familiarity with Cabri program; knowledge of the definition of locus.
NCTM Standards addressed:
Analyze characteristics and properties of 2 dimensional geometric objects; select and use
different representational systems, including coordinate geometry and graph theory; recognize
the usefulness of transformations and symmetry in analyzing mathematical situations; use
visualization and spatial reasoning to solve problems both within and outside mathematics.
Learning objectives:
The students will construct a compound locus.
Materials needed:
Cabri program
Suggested procedure:
Split students into groups of two or three and have them complete the worksheet.
Project AMP
Dr. Antonio R. Quesada – Director, Project AMP
Compound Locus
Group Member’s names: ______________________________________________________
File name: _________________________________________________________________
Goal: The students will gain a better understanding of loci and how to work with multiple
loci in order to solve a real-world problem.
Problem: A treasure is buried in your backyard. Your backyard contains a teepee, a tree, and
a stump. The teepee is 4 units from the stump and 9 units from the tree. The
treasure is equidistant from the teepee and the tree and also 5 units from the
stump. Construct a diagram of this using Cabri, following the directions below, and
locate all possible points of the buried treasure.
1. Open a new figure and using the Numerical Edit tool create the numbers 4, 9, and 5
in the upper right hand corner of the screen.
2. Create a point in the upper right of the screen and label this point Teepee. Use the
Measurement Transfer tool to create a point 9 units away from the point Teepee.
Label this point as Tree (place this point to the left and down from point Teepee).
3. Use the Measurement Transfer tool again to create a point 4 units away from the
point Teepee. Label this point as Stump (Place this point below point Teepee).
4. Your figure should resemble the one below: (make sure your points are in the same
general area of the points in the figure)
Project AMP
Dr. Antonio R. Quesada – Director, Project AMP
5. The treasure chest is buried in a spot that is equidistant from the teepee and the tree.
Find all the points that are equidistant from the teepee and the tree.
6. The treasure chest is also buried 5 units from the stump. Find all the points that are 5
units from the stump.
7. You should now be able to locate all the possible points of the buried treasure.
8. A compound locus is a collection of points common to two or more different locii.
From what you’ve just seen, how do you find these points?