All Swimmed Out

Suppose Sammy the swimmer at the tip of pier H wants to swim to the tip of pier I. Pier H is 2 km long and pier I is 1 km long. Since the swim is very long from H to I, Sammy thinks he will need to stop off at the beach to take a break (at point J). Sammy can stop at any point on the beach between the two piers (drag point J around once you construct this in a geometry software or view the java applet below). If Sammy takes the break, where should he stop on the beach if he wants to swim the least distance (the blue path) for the entire trip? What is the shortest distance Sammy can swim for the entire trip?
Use a geometry software to model the situation. If you do not have access to a geometry software, and your web browser is java-enabled, then view this java applet in a different window.

How might you determine the answer without technology? For students in algebra, how might you use a function and graphing calculator to determine the answer?