We care of the case when these distances have exactly two different values.

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 ?

Solution

"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 ?

Solution

With three values for distances ?

6 points ? That is put 6 points at two values for all the distances.