# JMAP Worksheets by Topic LOGIC: Locus

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```							Locus HW                                                                                              Page 1
Name: __________________________________

1     The locus of points equidistant from the points (4,-5) and (4,7) is the line whose equation is
(1) y = 1                   (3) x = l
010830   (2) y = 2         (4) x = 4
a
2     Dan is sketching a map of the location of his house and his friend Matthew's house on a set of
coordinate axes. Dan locates his house at point D(0,0) and locates Matthews house, which is 6 miles
080634   east of Dan's house, at point M(6,0). On the accompanying set of coordinate axes, graph the locus of
a        points equidistant from the two houses. Then write the equation of the locus.

3     Which equation represents the locus of points 4 units from the origin?
(1) x = 4                          (3) x + y = 16
2     2                     2     2
080426   (2) x + y = 4              (4) x + y = 16
a
Locus HW                                                                                              Page 2
Name: __________________________________

4       A city is planning to build a new park. The park must be equidistant from school A at (3,3) and
school B at (3,-5). The park also must be exactly 5 miles from the center of town, which is located
fall0837g   at the origin on the coordinate graph. Each unit on the graph represents 1 mile. On the set of axes
e           below, sketch the compound loci and label with an X all possible locations for the new park.

5       How many points are equidistant from two parallel lines and also equidistant from two points on
one of the lines?
010527a     (1) 1                    (3) 3
(2) 2                    (4) 4

6       What is the total number of points equidistant from two intersecting straight roads and also 300
feet from the traffic light at the center of the intersection?
080203a     (1) 1                         (3) 3
(2) 2                         (4) 4

7       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 treasure is buried 3 feet from the
010127a     fence and equidistant from the two trees.

a Sketch a diagram to show all the places where the treasure could be buried. Clearly indicate in
your diagram where the treasure could be buried.
b What is the distance between the treasure and one of the trees?

8       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.
010020a     (1) 1                      (3) 3
(2) 2                      (4) 4

```
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