Quadrants · Superchallenge problem

In a town whose streets form a grid, Mia's house is at the corner $(-4, -1)$ and her school is at the corner $(2, 3)$. She walks only along the streets. She wants to stop at a shop on the way, and the trip house $\to$ shop $\to$ school should be no longer than the shortest walk straight from house to school. Shops are only at street corners (points with whole-number coordinates). How many street corners, not counting the house and the school themselves, would work for the shop?