how to prove Q is the middle point of the segment PQ

Problem 10. 10. Take a 4-gon, ABC'D. Let K, L, M, N be the middle point at the segment AB , B C , CD, CA correspondingly. Let Q be the point of intersection of the lines LN and KM. Let P and Q be the middle point at the diagonal AC and BD correspondingly. Prove that Q is the middle point of the segment P