Name:_____________________________
Geometry Lesson 4-3 Compound Locus
1) Point P is located on AB . a) Describe the locus of points that are
(1) 3 units from AB
(2) 5 units from point P b) How many points satisfy both conditions in part a ?
2) In the coordinate plane, what is the total number of points 3 units from the origin and equidistant from both the x - and y -axes?
3) How many total points are equidistant from the x-axis and y-axis
and also 2 units above the x-axis?
4) How many total number of points are 5 units from the point (4,-2) and 2 units from the x-axis?

5) Celina is sketching a map of the location of her house and her friend
Madison’s house on a set of coordinate axes. Celina locates her house at point C (0,0) and locates Madison’s house, which is 6 miles east of Celina's house, at point M (6,0).
On the accompanying set of coordinate axes, graph the locus of points equidistant from the two houses and also 2 units (blocks) from the x-axis (Cocoa Lane). a) Write the equations of each locus. b) Find the coordinates of intersection of the loci.
6) a) Write the equation and sketch the locus of points that are “p” units from the origin.
b) Write the equation(s) and sketch the locus of points that are 2 units from the line x

4 c) How many points satisfy both conditions in
parts a and b when
1) p = 1?
2) p = 2?
3) p = 4?

7) On the set of axes provided below, sketch a circle with an equation
( x

2 )
2 
( y

1 )
2 
9 and also sketch the graph of the line 2x + y = 8.
What is the total number of points of intersection of the two graphs?
1) The locus equidistant from 2 houses 4 miles apart
2) The locus equidistant from 2 intersecting roads
3) The locus the same distance from 2 buildings that are 40 feet apart
4) The locus 3 feet from a tree
5) The locus 2 inches from a given line