How might the slow drifting of continents have caused the extinction of the dinosaurs?

Its mostly because of climate change. Example: the sea of Tetis (located where the Sahara stands today) was home for whales and megalodon (the giant shark). When continents shifted, whales moved north and south to colder waters where their food lived. Since whales were megalodon´s prey, and apparently the shark didn´t adapt to colder waters, it went extinct. Same thing could have happened to different species of dinosaurs. Just imagine changing vegetation, different weather, water availability, etc.