Where to wait for the post office next to the road

Some distance from the highway, running in a straight line here, there are two villages. There is a post office on the road. The village leaders made an appointment, that one day one, on the second day they will send a messenger; the messenger will pick up the mail and bring the letters to a neighbor first, which the mail brought for him, then he will return to his village with the rest of his correspondence.
Where should the messenger be on the road?, to take the shortest path in these peregrinations?
This issue is not without significance, because if we suppose, that the messenger imposes unnecessarily though only 100 meters of road a day, this minor inaccuracy would have made 36½ kilometers unnecessary over the course of a year, sole stripping and waste of time.

tmp5495-1If we mark the road with the MN line, and the villages with points A and B, then to find the desired point on the road, from point A it is necessary to take it perpendicular to MN and from the point of intersection S set aside SA1 = SA, then connect the straight line B with A1. Then the intersection of this line with the road will give the desired point C.

It could be pictured graphically, as follows: let's imagine, that along the road there is a huge mirror facing the village. Then the messenger leaving B should follow in a straight line towards the reflection of the village of A in the mirror - and vice versa: the messenger from A should go to B as seen in the mirror. They both will then reach the point C they are looking for.