Sample Response: I made a line segment that connected points A and B. I then used the compass setting to make circles with a radius of AB from each endpoint (Gaithersburg/Germantown and Manhattan).  This helped me find two points that were equidistant to each hometown.  When I construct a line through those two points, I can find the set of all points that are equidistant from Gaithersburg/Germantown and Manhattan.  Any town that lies on that line, the perpendicular bisector, would be an ideal location for the family reunion.[br][br]Alternative Answer: I used the segment tool to connect points AB to make a line segment. Then I clicked on the perpendicular bisector button. As I reselected the endpoints of A and B the bisector appeared automatically. This allowed me to find the set of all points that are equidistant from Gaithersburg/Germantown and Manhattan.  Any town that lies on that line, the perpendicular bisector, would be an ideal location for the family reunion.

Sample Response:[br]Since the perpendicular bisector helped me locate the set of all points that are equidistant from Gaithersburg and Manhattan, I know that any point that does not lie on this line is not equidistant from the two hometowns.  Since Philadelphia, PA is on the right side of the line, I know that it is closer to Manhattan, NY than Gaithersburg, MD.

West Chester, PA is directly between Gaithersburg and Manhattan.  I know because it lies on the perpendicular bisector, and is the midpoint of the segment joining the two hometowns.

Yes.  These cities also lie on the perpendicular bisector and are equidistant from the two hometowns. [list][*]Danville, PA[/*][*]Reading, PA [/*][*]Millville, NJ[/*][/list]