The authors use rhetorical devices to increase the credibility of the essay. This is the most correct answer of all those mentioned because it directly corresponds to ethos, the rhetorical appeal to credibility.
"Let every nation know, whether it wishes us well or ill, that we shall pay any price, bear any burden, meet any hardship, support any friend, oppose any foe to assure the survival and the success of liberty." (A) contains a hyperbole.
In literature, a hyperbole is a stylistic exaggeration. It is used to give a dramatic effect to a statement.
Here, the hyperbole is: "pay any price, bear any burden, meet any hardship, support any friend, oppose any foe." There are of course prices that the U.S. are going to refuse to pay, burdens they will not afford to carry, etc., but by exaggerating these commitments, Kennedy sounds more resolute and more persuasive.
Latin? i assume since most of our words originate from latin