2. 1. 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 Matthew’s house, which is 6 miles east of Dan's house, at point M(6,0). On the accompanying set of coordinate axes, graph the locus of points equidistant from the two houses. Then write the equation of the locus. DM

3. 2. 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(3) 3 (2) 2(4) 4 6 6 8 mm l m A

4. 3. The length of AB is 3 inches. On the diagram below, sketch the points that are equidistant from A and B and sketch the points that are 2 inches from A. Label with an X all points that satisfy both conditions. 1.5” 2” 1.5” A B

5. 4. 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

6. 5.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 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? 3’ 4’ 3’ 4’ 3’ 5’

7. 6. 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. T S 10’ 7’ 5’

8. 7. 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(3) 0 (2) 2(4) 4

13. 15. b. equidistant from two parallel lines. a. equidistant from two points. d. equidistant from two intersecting lines. e. At a given distance d from a line. c. At a given distance d from a point The locus of points is a line parallel to the given lines midway between them. The locus of points is the perpendicular bisector of the segment formed by joining the points. The locus of points is a pair of lines that bisect the angles formed by the intersecting lines. The locus of points is a pair of lines, parallel to original line on either side at a distance d from the line. The locus of points is a circle centered at the point with a radius of d.