Final answer:
The United States bought the southern portion of Arizona and New Mexico from Mexico in the Gadsden Purchase.
Step-by-step explanation:
The United States bought the southern portion of Arizona and New Mexico in the Gadsden Purchase from Mexico. The purchase was confirmed by the Mesilla Treaty signed in 1854. The United States paid $10 million for approximately 30,000 acres of land in Arizona's Mesilla Valley.