The point about 'a' and 'the' is not grammar. It is about what you want to say. You presumably know what trips you are talking about, we don't. If there was one trip, and the person you are talking to knows which trip you are talking about, then use 'the'. If you don't know how many trips the person might have been on, or you don't even know if they have been on a trip, then use 'a'. In most cases when you would say this, you would be talking to someone about a recent trip they went on. You know they went on the trip, so you use "the" to say "I'm talking about the obvious trip that we both are thinking about".

The right answer is: "on the trip", or "on your trip". If you use "on the trip" or "on your trip" it implies that you are speaking on a specific trip that you know that the other person was on. But if you use "on a trip" it implies that you are not talking about a specific trip. It doesn't make sense in this situation.