VTMO 2026 - Grade 9 - Final - SET 12 - Self-study Question 2

Let $ABCD$ be a quadrilateral. Choose $M$ on $AB$ and $N$ on $CD$ with $\dfrac{BM}{BA}=\dfrac{DN}{DC}$. Let $O$ be the midpoint of $MN$. Prove that $O$ moves on a fixed line.