This problem is very easy, try to solve it when 4 * (n-1) + 1 points are given.

Another hint: imagine if you got n points and you could cheat and make them all respect each other by stretching or compressing the coordinate grid (while keeping the points static); what would be the simplest way to transform the grid? In this problem you can't cheat like that, but on the other hand you only need to have n/5 points work together.