Final answer:
During a cesarean birth, the Foley catheter drainage tube and catheter bag should be positioned at the foot of the surgeon under the sterile drapes.
Step-by-step explanation:
During a cesarean birth, the nurse should position the Foley catheter drainage tube and catheter bag at the foot of the surgeon under the sterile drapes. This ensures that the catheter remains sterile and out of the way during the procedure. Positioning it near the head of the table or on top of the patient's leg would not be appropriate.