Final answer:
On December 28, 1848, the Treaty of Guadalupe Hidalgo was signed, ending the Mexican-American War and shaping the borders of the United States.
Step-by-step explanation:
On December 28, 1848, the United States President James K. Polk signed the Treaty of Guadalupe Hidalgo, which ended the Mexican-American War. The treaty established the Rio Grande as the Texas-Mexico border and ceded vast amounts of land from Mexico to the United States, including California, Nevada, Utah, Arizona, New Mexico, and parts of Colorado and Wyoming. This event played a significant role in the westward expansion of the United States and the overall shaping of the country's borders.