# SOLUTION: i am having trouble on finding the point equidistant for a triangle. the problem comes from a math book but i am not sure how i need to start it or work it. PROBLEM: A softba

Algebra ->  Algebra  -> Length-and-distance -> SOLUTION: i am having trouble on finding the point equidistant for a triangle. the problem comes from a math book but i am not sure how i need to start it or work it. PROBLEM: A softba      Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Geometry: Length, distance, coordinates, metric length Solvers Lessons Answers archive Quiz In Depth

 Question 360558: i am having trouble on finding the point equidistant for a triangle. the problem comes from a math book but i am not sure how i need to start it or work it. PROBLEM: A softball team named the Prairie Dogs is trying to decide where to have its annual team banquet. The players live in three different towns: Buck Springs, Boyce Mills and Ryan Falls. No player wants to travel further than any other. By looking at a map they decide that the banquet should be in one of four places: Morgan City (6,8), Lerchburg (5,9), Flegalville (5,7) or Davistown (8,8). Find by construction which of these towns is equidistant from the three home towns. Then find algebraically the coordinates of the point equidistant from the three home towns. Check your results by finding the straightline distance between your point and the three home towns. The coordinate are: Buck Springs (1,3), Ryan Falls (11,3), and Boyce Mills (7,15). Thank you for your help!!!!!! Answer by Edwin McCravy(8911)   (Show Source): You can put this solution on YOUR website!``` The 3 black points are where they live, and the red points are the possible places for the banquet. It looks as though the red point MC(6,8) Morgan City is the one that's equidistant from the three black points: Now we will find algebraically a point which is equidistant from the three points where they live, WITHOUT ASSUMING that it is necessarily at Morgan City MC(6,8). Let the point P(p,q) be a point which is equidistance from all three black points. Then using the distance formula Distance from BS(1,3) to P(p,q) Distance from RF(11,3) to P(p,q) Distance from BM(7,15) to P(p,q) Setting the first two distances equal: Square both sides: Setting the first and third distances equal: Substituting Squaring both sides: So the point which is equidistant from the three towns where the players live is P(p,q) or P(6,8), and we see that this really is the point at Morgan City MC(6,8). Edwin```