A compound locus is a locus that involves two or more conditions.
To Find Points That Satisfy a Compound Locus:
1) Construct the locus of points for each condition on the same diagram.
2) Make certain to label each locus.
3) Mark the points where the loci intersect. These points satisfy both sets of conditions.
Examples:
1) Tom’s backyard has two grown trees that are 40 feet apart. Tom wants to plant new trees that are 30 feet from each grown tree. In how many different locations could Tom plant the new trees?
2) Two parallel lines are 8 inches apart. Point P is located on one of the lines. What is the number of points that are equidistant from the parallel lines and also 4 inches from P?
3) How many points are 3 units from the origin and 2 units from the y-axis?
4) How many points are equidistant from points A and B and also 4 inches from AB?
5) How many points are equidistant from two intersecting lines and also 3 inches from the point of intersection of the lines?
6) How many points are 4 units from the origin and also 4 units from the x-axis?
7) How many points are equidistant from points (2,1) and Q(2,5) and also 3 units from the origin?
8) What is an equation of the locus of the points equidistant from points A(3,1) and
B(7,1)?
9) The distance between points P and Q is 9 inches. How many points are equidistant from P and Q and also 4 inches from P?
10) The distance between points P and Q is 8 inches. How many points are equidistant from P and Q and also 4 inches from P?
11) Point A is 4 centimeters from like k. How many points are 1 centimeter from line k and 3 centimeters from A?
12) A tree is located 30 feet east of a fence that runs north to south. Kelly tells her brother Billy that their dog buried Billy’s hat a distance of 15 feet from the fence and also
20 feet from the tree. a) Draw a sketch to show where Billy should dig to find his hat.

b) How many locations for the hat are possible?
13) Point P is x inches from line l. If there are exactly 3 points that are 2 inches from line l and also 6 inches from P, what is the value of x?
14) Point P is located on AB. a) Describe the locus of points that are 3 units from AB. b) Describe the locus of points that are 5 units from point P. c) How many points satisfy both conditions from above?
15) Lines AB and CD are parallel to each other and 6 inches apart. Point P is located between the two parallel lines and 1 inch from AB. a) Describe the locus of points that are equidistant from AB and CD. b) Describe the locus of points that are 2 inches from point P. c) How many points satisfy both conditions from above?
16) a) Describe completely the locus of points 2 units from the line whose equation is x = 3. b) Describe completely the locus of points n units from point P(3,2). c) What is the total number of points that satisfy the conditions in parts a and b simultaneously for n = 2?