Problem 4.5 Alex

Alex should locate his hut where he is an equal distance from the three different vertices of the island. This creates the smallest total distance to all three points added together. The first figure has his hut fixed at this locations and the second figure allows you to move his hut around to show how the total distance changes. At first I thought making it closer to the bottom two vertices would be the way to go but this does not hold true because then the distance from the third gets significantly greater.