VTMO 2026 - Grade 8 - Semifinal - SET 05 - Self-study Question 15

In the coordinate plane, rectangle $OMNP$ has vertices $O=(0,0)$, $M=(0,5)$, $N=(10,5)$, $P=(10,0)$. How many integer-coordinate points $(x,y)$ lie strictly inside it and satisfy $x+y<10$?