In what year was the U.S. Constitution written and signed?

The U.S. Constitution was written and signed in 1787, making this the correct choice. The Constitutional Convention convened in Philadelphia that year with the purpose of addressing the weaknesses of the Articles of Confederation, which had become apparent in governing the newly independent states. The delegates debated and drafted the Constitution over several months, ultimately signing it on September 17, 1787.

The other years mentioned are significant in U.S. history but pertain to different events. For instance, 1776 marks the signing of the Declaration of Independence, which declared the American colonies' separation from British rule. The year 1791 is significant because it is when the Bill of Rights, the first ten amendments to the Constitution, was ratified. Finally, 1801 is notable for the commencement of Thomas Jefferson's presidency, a period that came after the Constitution was already adopted. Thus, 1787 is specifically linked to the creation of the Constitution itself.