3 points :
There is only one pattern : a triangle. With one distance, only an equilateral triangle.
With two different distances, any isosceles triangle. That is the ratio of distances is undefined.
4 points, this becomes more interesting :
How many different patterns with two values of distances ? Ratio of these values ?
"Of course" we can't put 4 equidistant points on a plane !
With 4 points and 3 values for distances, the problem becomes uninteresting, as for the 3 points and two values case...
5 points, with two values ?
With three values for distances ?
6 points ? That is put 6 points at two values for all the distances.