3.2.3 Lines on a plane

Problem: On the sides \( A B \) and \( A C \) of the given triangle \( A B C \) points \( M \) and \( N \) are taken respectively, that divide the segments \( A B \) and \( A C \) with respect to \( 3: 1 \) counting from the vertex \( A \), and the point \( Q \) is the midpoint of segment \( B C \). Prove that the straight lines \( A Q, B N, C M \) intersect at one point. Given the coordinates of the vertices of the triangle \( A B C: A(-3,-1), B(1,-5), C(9,3) \).