Answer:
A. half the distance between point A and point K
Explanation:
There are several assumptions we must make in order to answer the question:
- line x is parallel to line y
- FJIHG is a reflection of ABCDE across line x
- KLMNO is a reflection of FJIHG across line y
- AK is parallel to PQ
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