This made intuitive sense to me once you consider that the "L" function we defined is proportional to the perpendicular distance from the line. In previous lectures we just used this result to determine whether it was "above" or "below" the line, but the magnitude of the output is proportional to this actual distance. From this result, it is easy to see how this fraction is determined when using the basic rules of geometric similarity.
This made intuitive sense to me once you consider that the "L" function we defined is proportional to the perpendicular distance from the line. In previous lectures we just used this result to determine whether it was "above" or "below" the line, but the magnitude of the output is proportional to this actual distance. From this result, it is easy to see how this fraction is determined when using the basic rules of geometric similarity.