I formulated a question badly, sorry. I'll try to reformulate.

There is a road (as polyline layer with WGS_1984_Web_Mercator coordinate system) on the map. And on the 9500 meters from the beginning of the road is some object, which place on the road I must to find (point geometry). Assume for simplicity - the road is straight.

If I measure the distance between the kilometer posts, using the tool "Measure" with the "Planar" option, I get the 2314 meters, and with the "Geodesic" option - 1000 meters. By default in arcmap is used "Planar" option as I use WGS_1984_Web_Mercator , and I manually switch mesure instrument to "Geodesic" option.

Now I try programmatically to define coordinates of the object on the road with using the following expression to calculate the lengths of the segments:

public double Length()
{
return Math.Sqrt(Math.Pow(Point2.X - Point1.X, 2) + Math.Pow(Point2.Y - Point1.Y, 2));
}

I guess that to correctly use the distance of the object from the beginning I must use a conversion ratio (approximatly ration = 2,314 for my case) , ie,

distance = 9500 * ratio ;

If so, how do you know this ratio for a given point of the map?