This visual trace shows how to use APIRouter in FastAPI to organize routes modularly. First, an APIRouter instance is created. Then, routes like GET '/hello' are defined on this router. Next, a main FastAPI app is created. The router is included into the main app using app.include_router(router). When the server runs and receives a request matching '/hello', the router's handler function say_hello is called, returning a JSON response. This modular approach helps keep route code clean and separated. Variables like 'router' and 'app' change state as routes are added and included. Key moments include understanding why routers are used, how inclusion connects routes, and how requests trigger router handlers. The quiz checks understanding of router state, inclusion step, and adding routes. The snapshot summarizes the modular routing pattern with APIRouter.