Correct answer: Mexico
Context/detail:
The Mexican Cession was territory ceded (meaning given up) to the United States in 1848 after the Mexican-American War. The territory included lands that represent the full states of California, Nevada, and Utah, as well as large portions of Arizona and New Mexico, and about a quarter of what would become the state of Colorado. There was also a small section of Wyoming involved. So that represents the bulk of territory that is in Southwest of the present United States.
The US also had obtained a large portion of land from France in 1803, in what was termed "The Louisiana Purchase." That stretch of territory was in the middle section of the present United States (not in the Southwest). The Louisiana Purchase stretched from Louisiana northward to cover present-day states of Arkansas, Oklahoma, Missouri, Kansas, Nebraska, Iowa, and more. It did include portions of what would become Western states of New Mexico, Colorado, Wyoming and Montana.