The signing of the Residence Act on July 16, 1790, approved the creation of a capital district located along the Potomac River on the country's East Coast. As permitted by the U.S. Constitution, the District is under the exclusive jurisdiction of the Congress and is therefore not a part of any U.S. state.And then simply read the 10th Article.
What about Article IV, Section 3? “The Congress shall have power to dispose of and make all needful Rules and Regulations respecting the Territory or other Property belonging to the United States; and nothing in this Constitution shall be so construed as to Prejudice any Claims of the United States, or of any particular State.” That doesn’t limit it to the D.C. area.