. Which of the following territories were key to a railroad line existing in the Southwestern United States?
mexican cession and gadsden purchase

The Gadsden Purchase (Spanish: la Venta de La Mesilla "The Sale of La Mesilla")[2] is a 29,670-square-mile (76,800 km2) region of present-day southern Arizona and southwestern New Mexico that the United States acquired from Mexico by the Treaty of Mesilla, which took effect on June 8, 1854. The purchase included lands south of the Gila River and west of the Rio Grande where the U.S. wanted to build a transcontinental railroad along a deep southern route, which the Southern Pacific Railroad later completed in 1881–1883. The purchase also aimed to resolve other border issues.

The first draft was signed on December 30, 1853, by James Gadsden, U.S. ambassador to Mexico, and by Antonio López de Santa Anna, president of Mexico.[1] The U.S. Senate voted in favor of ratifying it with amendments on April 25, 1854, and then transmitted it to President Franklin Pierce. Mexico's government and its General Congress or Congress of the Union took final approval action on June 8, 1854, when the treaty took effect. The purchase was the last substantial territorial acquisition in the contiguous United States, and defined the Mexico–United States border. The Arizona cities of Tucson and Yuma are on territory acquired by the U.S. in the Gadsden Purchase.

The financially strapped government of Santa Anna agreed to the sale, which netted Mexico $10 million[3] (equivalent to $230 million in 2019[4]). After the devastating loss of Mexican territory to the U.S. in the Mexican–American War (1846–48) and the continued filibustering made by New Mexico governor William Carr Lane in the zone, some historians argue that Santa Anna may have calculated it was better to yield territory by treaty and receive payment rather than have the territory simply seized by the U.S.[5]

Explanation:

the answer to your question is true