AVI310104
Why FROM/TO Is a Reciprocal
One Line, Two Directions
In Concept 2, you drew compass crosses at two points and measured the return bearing. In Concept 3, you learned that reciprocal bearings are always 180° apart. Now let's see why these are the same thing.
The Key Insight
The bearing line from A to B and the bearing line from B to A are the same line — the arrows just point in opposite directions.
This means "bearing of B from A" and "bearing of A from B" are reciprocals. They must differ by exactly 180°.
Pick Any Point on the Line
Draw any bearing line between two points. Now pick a new point anywhere on that line and draw a compass cross there. Measure the bearing in both directions.
You will always get the same two bearings — and they are always 180° apart. It does not matter where on the line you stand. The line itself has a fixed direction, and the opposite direction is always the reciprocal.
The Connection
"Bearing of B from A" and "bearing of A from B" are opposite directions on the same line
Opposite directions on the same line always differ by 180°
Therefore, "bearing of B from A" and "bearing of A from B" are always reciprocals
The compass cross method (Concept 2) and the ±180° shortcut (Concept 3) are not two separate ideas — they are the same idea seen from two perspectives.
Back Bearing = Reciprocal — Why?
Step through the proof: measure A→B, then B→A, then place C in the middle and measure again. The bearings match — back bearing IS the reciprocal. [avi-back-bearing-proof]