A. half the distance between point A and point K
There are several assumptions we must make in order to answer the question:
Let P' and Q' be points on lines x and y where the line AK intersects those lines, respectively. The distance P'Q' will be the same as the distance PQ. (They are opposite sides of rectangle PP'Q'Q.)
By the nature of reflection, AP' = P'F, and FQ' = Q'K. We know that ...
... AK = AP' +P'F +FQ' +Q'K
By substitution, this becomes ...
... AK = P'F +P'F +FQ' +FQ' = 2P'F +2FQ' = 2(P'F +FQ')
We also know that ...
... P'F +FQ' = P'Q' = PQ
so ...
... AK = 2·PQ
... AK/2 = PQ . . . . . divide by 2
