which route on the map did Vasco da Gama use in his search to find a new way to Asia?

The correct option is, The bottom one because he went around Africa.
Vasco da Gama, was a famous Portuguese navigator and explorer. In the age of the discoveries he stood out for having been the commander of the first ships that sailed directly from Europe to India, the longest ocean voyage ever made.
From the beginning of the 15th century, driven by the Infante Enrique, the Portuguese had been deepening their knowledge of the African coast. Since the 1460s, the goal was to get around the southern tip of the African continent to access the riches of India - black pepper and other spices - establishing a reliable maritime route.