Final answer:
Iago leaves Roderigo to preserve his deceptive appearance of loyalty to Othello, allowing him to continue his manipulative schemes without arousing suspicion.
Step-by-step explanation:
Iago leaves Roderigo at Brabantio's house rather than waiting for Brabantio to come down because Iago wishes to maintain his appearance of loyalty and good standing with Othello.
While he instigates Roderigo to alert Brabantio of Desdemona's elopement with Othello, Iago does not want to be seen as involved in this scheme. By distancing himself from Roderigo's actions, Iago can continue his manipulative plot without raising suspicion, preserving his deceptive facade in Othello's eyes.