Curiously, to me (U.S. native speaker) "make a trip" is common, but has a slightly different meaning--it means a short, everyday trip, and errand. "I need to make a trip to the supermarket to pick up some bread." However, for a long trip, like a vacation or a business trip, I use "take." "I need to take a trip in August so that I can attend the business convention."

"Take a trip " or " go on a trip " You can say " make a journey to a certain destination " but ' make a trip ' is not really used , although it is not necessarily wrong !!

"Take a trip" is most commonly used.