The root "alter· has mainly two meanings different "to change, alter, vary" which comes from Old French, and "the other (of the two)" whose origin comes from Latin. In the sentence, "Other" is the one that helps define the word "alternate" as this word is used when there are two options, and one of them is designated to take the place of the other, as it is in the case of the sentence: They had to take other route.
