Five major buildings on a campus have coordinates A(0,0), B(0,800), C(200,1000), D(400,800), and E(400,0) (where the x and y axes are scaled in units of meters). Roads must be constructed to connect all of these buildings at a cost of $32 per linear meter (using a standard road width).

So, for example, if the point F has coordinates (200,400) and straight roads are built between A & F, B & F, D & F, E & F, and C & D, almost 2072 meters of road would be needed to connect the buildings at a cost of $66,294. to the nearest dollar.

Given a road construction budget of $55,900. for this project, show how you might connect the buildings within the budget constraints.

Made using geometer's sketchpad:

http://www.mohawk.mtrsd.k12.ma.us:8000/site/dept/math/jgalvagni/pid5367.jpg

Its hard to describe the steps used to draw this but here goes:

Basically H was picked to set angle BHC at 120 degrees which allows H to be anywhere on the arc of a circle of which BC is a 120 degree arc.  Set a ray out from H at 120 and use D and H to define point G in the same manner as H was picked.  Send a ray down from G.

Use A and E to set point F wher the ray from G crosses its arc.  Adjust H until the ray going down to the left from F passes through A.

Posted by Jer on 2007-02-05 12:12:58