In what part of the leguminous plant do nitrogen-fixing bacteria live?
 

Roots are part of the leguminous plant where nitrogen-fixing bacteria live.

Nitrogen fixation is a process by which certain plants, such as legumes, form a mutually beneficial relationship with nitrogen-fixing bacteria. 

In legumes, such as soybean, pea, or clover, nitrogen-fixing bacteria live in specialized structures called nodules that are located on the roots of the plant. The nodules are formed as a result of the interaction between the plant and the bacteria. The plant provides the bacteria with carbohydrates, and in return, the bacteria convert atmospheric nitrogen gas into a form that the plant can use, such as ammonia.

The nodules on the roots of leguminous plants are important for nitrogen fixation and can help to increase soil fertility and crop yields.