VTMO 2026 - Grade 9 - Final - SET 1 - Self-study Question 1

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