Why are two independent parameters necessary and enough for determining position of a point with respect to a reference point in a plane?
In other words, I want to address a point from another reference point in a plane. How many independent parameters are necessary and enough for that aim? And why?
To show the sufficient condition, you can reason as follows:
choose three points in the plane forming a non-degenerate triangle and choose two sides;
for any point, there are two unique lines parallel to the respective sides that pass through it;
the intersection points of the parallels with the sides can be unambiguously located by means of the ratio of lengths.
Conversely, two ratios define two non-parallel lines, that have a single intersection point.
By this method any point can be unambiguously designated by two real numbers.