Locus: Compound Loci Continued (a)
Problems:
1)
How many points in a plane are five units from a line and also equidistant from
two points on the line?
2)
What is the number of points in a plane two units from a given line and three units
from a given point on the line?
3)
On the set of axes below, sketch the locus of points that are 4 units from the origin
and sketch the locus of points that are equidistant from the lines x = -1 and x = 3.
Label with an X all points that satisfy both conditions.
4)
On the grid below, graph the points that are equidistant from both the x and y axes and
the points that are 4 units from the origin. Label with an X all points that satisfy both
conditions.
5)
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?
6)
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?
7)
How many points are 4 units from the y axis and 1 unit from the origin?
8)
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?
9)
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?
10)
How many points are 4 units from the origin and also 4 units from the x-axis?
11)
How many points are equidistant from points (2,1) and Q(2,5) and also 3 units
from the origin?
12)
(a)
(b)
(c)
(d)
Describe fully the locus of points 2 units from the y-axis.
Describe fully the locus of points 4units from the origin.
Find the number of points that simultaneously satisfy the conditions in
part a and b.
Find the coordinates of all points that simultaneously satisfy the conditions
in part a and b.
13)
Two points M and N are 6 inches apart. How many points are there that are 12
inches from M and also 5 inches from N?
14)
Jack’s backyard has two grown trees that are 40 feet apart. Jack wants to plant
new trees that are 20 feet from each grown tree. In how many different locations
could Tom plant the new trees?