How did they choose Washington D.C. as the capital?

Answer 1

Article One of the Constitution provides for a federal district, separate from the states, to serve as the capital of the United States. The location of the federal district was the subject of heated debate however. In what later became known as the Compromise of 1790, James Madison, Alexander Hamilton and Thomas Jefferson came to an agreement that the federal government would assume debt incurred by the states during the Revolutionary War on the condition that the new national capital be located in the South.

The Residence Act of 1790 subsequently authorized the creation of the federal district at a site along the Potomac River to be selected by George Washington.

Answer 2

He was chosen for the state capitol because they thougt he was a good man and he did not lie.