The Coordinate Plane · Superchallenge problem

On a town grid you can only walk along the streets (straight across or straight up and down), so the walking distance between two corners is (blocks across) + (blocks up or down). Amy lives at $(2, 2)$ and Ben lives at $(8, 6)$. How many street corners $(x, y)$, with $x$ and $y$ each a whole number from $0$ to $10$, are the same walking distance from Amy's house as from Ben's?