Name: ______Lab #20
Ms. Schwartz Math A Year 2 Lab
Compound Locus
*****Must draw a picture for credit*****
1. What is the number of points in a plane 2 units from a given line and 3 units from a given point on the line?2. Two points A and B are 6 units apart. How many points are there that are 3 units from point A and also 5 units from B?
3. What is the number of points in a plane 4 units from a given line and 1 unit from a given point on the line?
4. Two points D and E are 10 units apart. How many points are there that are 2 units from A and 6 units from B?
5. Two points A and B are 6 units apart. How many points are there that are equidistant from both A and B and also 5 units from A?
6. Parallel lines r and s are 8 meters apart, and A is a point on line s. How many points are equidistant from r and s and also 4 meters from A?
7. A given point P is 10 units from a given line. How many points are 3 units from the line and 5 units from point P?
8. 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?
9. 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.
(1) 1 (3) 3
(2) 2 (4) 4
10. How many points are equidistant from two parallel lines and also equidistant from two points on one of the lines?
(1) 1 (3) 3
(2) 2 (4) 4
11. Point P lies 8 centimeters from line How many points are both 2 centimeters from line and 8 centimeter from point P?
(1) 1 (3) 3
(2) 2 (4) 4
12. In the coordinate plane, Draw the locus of points 5 units from the origin. Then draw the locus of points equidistant from both the x-axis and y-axis. What is the total number of points 5 units from the origin and equidistant from both the x- and y-axes?
13.
a. Draw the locus of points equidistant from the points (4,1) and (4,5) and write the equation for this locus.
b. Draw the locus of points equidistant from the points (3,2) and
(-4,2) and write the equation for this locus.
c. Find the number of points that satisfy both conditions stated
in a and b. Give the coordinates of each point found.
14.
a. Draw the locus of points 3 units from the y-axis and write the equation for this locus.
b. Draw the locus of points 4 units from the origin and write the equation for this locus.
c. How many points that satisfy both conditions stated
in parts a and b?
15. 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?
16. 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.
17. 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.