I wrote 'endelig' instead of 'endelige' and was wondering why my answer was wrong. Maybe you had a similar thought, so I want to share my solution: 'svar' is singular, but it is definite, so that's why to use 'endelige'. It is not ANY answer, but YOUR answer. If one writes the following, it is probably more obvious: 'Er det det endelige svaret ditt?'. I guess the sentence DL suggests is more common because one avoids the double 'det'.
As far as the ending "-e" is concerned AFAIK you must use it every time the adjective follows an article (det) or possessive adjective (ditt), so no need to analyse it further: depending on which possessive construction you prefer there is either a det or a ditt before "final" so it must be endelige.