Shortest Distance Question

Question

A utility company is running new power lines to two cottages. On a site plan, the cottage have coordinates A (6,7) and B (13, 6) and the closest transformer is at T (13,14). The utility will run a line straight from the transformer to one of the cottages and then connect the other cottage to that line using the shortest possible route.
a) Draw a diagram on a grid to show the two possible ways to run the power lines.
b) Determine which route will require the least cable

 

Please help!!!

Answer 1

This problem requiresyou to make a drawing (read part a).  It is much easier to solve with that picture.  Also, you can visualize what math puts in letters and symbols.

 

The two ways to supply power from T to both A and B is (1) to go from T to A then from A to B or (2) to go from T to B then from B to A.  These two distances may be found by looking at the coordinates of the points and using the Pythagorean theorem to find each hypotenuse  (this seems to be why it is a math problem).

 

After finding the two total d distances, it's not to hard to choose the route that uses the least cable (although computers do this in a very elaborate, yet very fast, way).