
Ed M. answered 02/24/16
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This is a good question. While it is true that verbs like prevent, fail, stop, avoid and deny share an element of meaning in some of their senses that could be characterized as "negative," i.e., they bring an implication that another action was "not" carried out, this "negation" is grammatically and semantically not the same as the logical notion of negation in grammar, which is always expressed in English through the use of the explicit negative particle not or its contraction n't and/or explicitly negative words like none, nothing, nowhere etc., and even sometimes with a few words that don't "look" negative, i.e., they don't have any -n- element, but still have logically negative force, e.g., hardly and seldom.
This is all to say that the sentence John* prevented Mark from entering his room is grammatically not negative, and not really even semantically so; as proof, note that we can easily negate (the main verb of) the sentence which will yield the perfectly grammatical John didn't prevent Mark from entering his room. Of course one of the semantic implications or inferences of the former sentence is that Mark didn't enter his room, but again this has no effect on the overt structure of the sentence this proposition is embedded in, namely John prevented __. (Conversely, John didn't prevent Mark from entering his room implies--albeit less strongly--that Mark entered his room.)
That said (and typically for me, it's a lot), if you refer again to the rules I previously gave you for forming tag questions (https://www.wyzant.com/resources/answers/189129/question_tag_question), the correct tag for John prevented Mark from entering his room is didn't he since the main verb of the sentence is affirmative past tense prevented, and thus by the rules for making tag questions in English you will (1) add do-support for the verb prevent, (2) change do to past tense did since prevented is in the past tense and (3) change John to the appropriate subject pronoun he.
*I changed "Join" in your original as I have never heard of anyone given this as a personal name, though verbs that are homophones of certain names are not uncommon, e.g., Tab Hunter, Spike Lee and Rush Limbaugh. [waiting pathetically, like Jeb Bush, for applause for my eclectic selection of examples]