I just did a phone screen with Meta, and the interviewer asked for Euclidean distance between two points; they definitely have some nerds in the building.
E: wasn't the only one.
https://en.wikipedia.org/wiki/Nearest_neighbor_search
edit: If you want to use a heap, the general solution is to define an appropriate cost function; e.g., the p-norm distance to a reference point. Use a union type with the distance (for the heap's comparisons) and the point itself.