Why did Aztec build their city?

In the beginning they were a nomadic tribe, traveling from the north to the south of what we now know as Mexico. They had a prophecy saying that they should build their city where they saw the divine signal of an eagle devouring a rattle snake. The legend says they saw that signal in the middle of a big lake named Texcoco. As the prophecy stated that, they decided to build their city there, so they began building the city in the lake, so it was kind of a floating city. They named the city Tenochtitlan.