NAME_______________________________________________DATE_____________
GEOMETRY
LOCUS (REGENTS QUESTIONS)
MRS. BINASO
Draw a diagram for each of the following on graph paper or loose leaf.
(Homework will be unacceptable if not accompanied with diagrams.)
PART I:
1. The locus of the midpoints of the radii of a circle is
(1) a point
(2) two lines
(3) a line
(4) a circle
2. How many points are equidistant from two intersecting lines, l and m, and 3 units
from the point of intersection of the lines?
(1) 1
(2) 2
(3) 3
(4) 4
3. The distance between points P and Q is six units. How many points are equidistant
from P and Q and also three units from P?
(1) 1
(2) 2
(3) 3
(4) 6
4. The distance between points P and Q is 8 units. How many points are equidistant
from P and Q and also 3 units from P?
(1) 1
(2) 2
(3) 0
(4) 4
5. The distance between parallel lines l and m is 12 units. Point A is on line l. How
many points are equidistant from lines l and m and 8 units from point A?
(1) 1
(2) 2
(3) 3
(4) 4
6. In the coordinate plane, what is the total number of points 5 units from the origin and
equidistant from both the x- and y-axes?
(1) 1
(2) 2
(3) 0
(4) 4
7. How many points are equidistant from two intersecting lines and 3 units from their
point of intersection?
(1) 1
(2) 2
(3) 3
(4) 4
8. An equation of the locus of points equidistant from the points (0,6) and (0,-2) is
(1) x = 2
(2) y = 2
(3) x = -2
(4) y = -2
9. If the graphs of x2 + y2 = 4 and y = -4 are drawn on the same set of axes, what is the
total number of points common to both graphs?
(1) 1
(2) 2
(3) 3
(4) 0
10. Which is an equation of the locus of points that are 3 units from the point (3,2)?
(1) (x  3)2 + (y  2)2 = 9
(3) (x  3)2 + (y  2)2 = 3
(2) (y  2) = (x  3) + 3
(4) y = 3x  7
11. What is the total number of points that the graphs of x2 + y2 = 16 and y = x have in
common?
(1) 1
(2) 2
(3) 0
(4) 4
12. Points M and N lie on line l. Line k is parallel to line l. The total number of points
equidistant from points M and N and also equidistant from lines l and k is
(1) 1
(2) 2
(3) 0
(4) 4
PART II:
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. How many locations for the lampposts are possible?
2. Steve has a treasure map, represented in the accompanying diagram, that shows two
trees 8 feet apart and a straight fence connecting them. The map states that the
treasure is buried 3 feet from the fence and equidistant from the two trees.
a. Using a separate sheet of paper, show all the places where the treasure could be
buried. Clearly indicate where the treasure could be buried.
b. What is the distance between the treasure and one of the trees?
3. A treasure map shows a treasure hidden in a park near a tree and a statue. The map
indicates that the tree and the statue are 10 feet apart. The treasure is buried 7 feet
from the base of the tree and also 5 feet from the base of the statue. How many
places are possible locations for the treasure to be buried? Draw a diagram of the
treasure map, and indicate with an X each possible location of the treasure.
4. An architect is deciding where to install a fountain in a long rectangular courtyard.
The fountain should be equidistant from the north and south sides of the courtyard. It
should also be 30 feet away from the entrance on the north side. The courtyard is 60
feet across. Create a map showing where the fountain should be installed.
Map of the Courtyard
North Entrance
60 ft.
South Entrance