I am remodeling the master bath and I need to relocate the bath tub. I will be extending the trap about 3-4' from where it is now. I'm wondering if I need to relocate the vent pipe as well. How far can it be from the vent?
It depends on the diameter of the trap. Under International Building Code use table 906.1.
A 1.5" trap can be 6 feet from the vent (if your trap is only 1.25" the maximum distance is 5 feet).
It looks like you should be fine in your situation.