This equation depicts the relative distance of a position point `P` from the origin of reference frame labeled `A`, based on knowledge of the distance between that reference frame `A` and another reference frame `B` and on knowledge of the distance of the same position point `P` from the origin of the reference frame `B`.

This simple examination of relative displacement is the basis for a mathematical depiction of relative velocity as well, and is the fundamental basis of relativity theory.

Usage

Essentially this equation helps you examine the situation where you have two observers moving in two separate reference frames.  It is important to represent the signs of the relative positions, so in the picture x-direction is positive to the right and negative to the left of the origins.

In the picture, a subject `P` is located instantaneously (and may possibly be moving) in a reference frame `A`.  The origin of the reference frame `A` is the point `O_A`.  Likewise, the same subject `P` is located instantaneously (and may possibly be moving) in a reference frame `B`. At this particular point in time, the distance of `P` from the origin `O_B` is known.  This distance is labeled `x_"B/A"`.

We also know the distance between origins `O_A` and `O_B` as  x_"B/A".  Knowing these two distances, we compute the distance of the subject `P` from the origin `O_A`.

See also

Relative Velocity