30. Landscaping The school board plans to construct a fountain in front of the school. What are all the possible locations for a fountain such that the fountain is 8 ft from the statue and 16 ft from the flagpole?

    

Make a drawing of each locus.

31. the path of a car as it turns to the right
32. the path of a doorknob as a door opens
33. the path of a knot in the middle of a jump-rope as it is being used
34. the path of the tip of your nose as you turn your head
35. the path of a fast-pitched softball

36. Reasoning Points A and B are 5 cm apart. Do the following loci in a plane have any points in common?

    the points 3 cm from A

    the points 4 cm from A B ¯ eh b bar

    Illustrate your answer with a sketch.

Coordinate Geometry Draw each locus on the coordinate plane.

37. all points 3 units from the origin
38. all points 2 units from ( − 1 , 3 ) open minus , 1 comma 3 close
39. all points 4 units from the y-axis
40. all points 5 units from x = 2 x equals 2
41. all points equidistant from y = 3 y equals 3  and y = − 1 y equals , minus 1
42. all points equidistant from x = 4 x equals 4  and x = 5 x equals 5
43. all points equidistant from the x- and y-axes
44. all points equidistant from x = 3 x equals 3  and y = 2 y equals 2
45. 1. Draw a segment to represent the base of an isosceles triangle. Locate three points that could be the vertex of the isosceles triangle.
    2. Describe the locus of possible vertices for the isosceles triangle.
    3. Writing Explain why points in the locus you described are the only possibilities for the vertex of the isosceles triangle.
46. Describe the locus of points in a plane 3 cm from the points on a circle with radius 8 cm.
47. Describe the locus of points in a plane 8 cm from the points on a circle with radius 3 cm.
48. Sketch the locus of points for the air valve on the tire of a bicycle as the bicycle moves down a straight path.

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