What factor promoted the rise of powerful east african city states abundant freshwater and farmland to support large populations control of interior peoples with access to abundant resources geographic barriers outside contact and invasion location along important trade routes

The fourth option is the right one. The Swahili city-states grew during the second half of the first millenium thanks to the intense trade activity in the Indian Ocean, India and China had been important trade centers since antiquity and a great trade network had been built over the centuries. Besides the connections between coastal cities of the Indian Ocean, in it's northern part, by the coast of Persia, passed the Silk Road, the trade route that connected Europe to China throughout the Middle Age.