Final answer:
The Swahili city-state that came to dominate the southern part of the coast and traded in gold with Sofala was Kilwa. It obtained wealth and power by controlling the rich gold trade from Sofala, and by the fourteenth century, it was the most significant city along the Swahili coast.
Step-by-step explanation:
The Swahili city-state that dominated the southern coast and traded in gold with Sofala was Kilwa. In the 1180s, the ruler of Kilwa gained control over the port city of Sofala, which became a wealthy and powerful conduit for the gold flowing from the mines of the Kingdom of Mutapa. Thanks to its control over the lucrative gold trade, Kilwa became the most prominent city-state along the Swahili coast, asserting its authority over other city-states including Mombasa, Zanzibar, and others.
By the early fourteenth century, Kilwa had established itself as the most significant city in the region, as attested by travelers like Ibn Battuta. Its dominance was such that when the Portuguese arrived in the late fifteenth century, they recognized Kilwa's preeminent position in the regional trade dynamics. Despite their efforts, the Portuguese were largely unable to dismantle Kilwa's extensive influence until later alliances and sultanates shifted the balance of power.