Calculate the distance from the beginning of the path to the point and determine the membership?

Question

Geometry

There is a set of geographic coordinates (Lat, Lon) that form a broken open line.
There is a point, it is necessary to determine whether it belongs to this line (With an error of 5-10 meters), and the distance to it from the beginning of the line.
The second question is quite trivial to solve - to calculate the distance to the last broken line on which the point was found by segments and from there to it, but perhaps there is a simpler algorithm?

Answer 1

What is the algorithm for determining the nearest segment of the path to a point?