A Highway Contractor Needs to Locate a Single Supply Point

Essay

A highway contractor needs to locate a single supply point to provide road building materials to four projects. The four projects, which are all approximately the same magnitude, are located at the following coordinates. Coordinate units are in miles.
$$\begin{array} { | l | c | c | } \hline & \mathrm { X } \text { (East) } & \mathrm { Y } \text { (North) } \\\hline \text { Project A } & 50 & 10 \\\hline \text { Project B } & 15 & 60 \\\hline \text { Project C } & 40 & 60 \\\hline \text { Project D } & 30 & 20 \\\hline\end{array}$$
a. On the grid below, plot the locations of the four road-building sites. Properly label all points.
b. What is the center of gravity?
c. If a single truck were sent from center-of-gravity to each project and back (four round trips), how many miles would be traveled?
(Hint: use the Pythagorean Theorem C = $\sqrt { A ^ { 2 } + B ^ { 2 } }$
).
d. Add the calculated center of gravity to the grid.