Final answer:
The Mexica, later known as the Aztecs, secured land to found Tenochtitlán by allying with local powers such as Culhuacán and the Tepanecs and forming the Triple Alliance. Their strategic location on Lake Texcoco's island facilitated growth into a dominant empire.
Step-by-step explanation:
The traditional narrative of Aztec migration holds that the Mexica, as part of their decades-long journey seeking a homeland, made several alliances that provided for their settlement. Initially allying with the city of Culhuacán and later the Tepanec state, they were granted the right to establish Tenochtitlán on an island in Lake Texcoco around 1325. This strategic location offered defensive advantages and fertile lands for agriculture. Through military service to surrounding powers and regional trade, the Mexica accrued wealth and influence. By 1428, they formed the Triple Alliance with Texcoco and Tlacopan, becoming the dominant force in central Mexico. Thus, the base for what would eventually be known as the Aztec Empire was formed, with Tenochtitlán at its center.