Observers move along their trajectories inclined to each other at angleϕ , where sinϕ is their relative velocity. Trajectories of bodies are, at the same time, the timeaxes of their frames. Spaceaxes of the frames are chosen so as to be perpendicular to the trajectory of the observed body. In case of mutual observation of the observers, connected with the xt and x't' frames, the xaxis is perpendicular to the t'axis and analogically the x'axis is perpendicular to the t axis. Axes of coordinates systems of both bodies are shown in the figure below
Let us put a point P in frames of both bodies  see the figure on the left. According to the picture, xcoordinate of the point P is equal to : where: then: And for coordinate t: where: then: 

As it has been shown above, the geometrical interpretation of FER allows to derivate the Lorentz Transformation in a very simple way. So, what is wrong in this derivation???


The choice of xaxis of xt coordinate system is equivalent to the statement saying that the point P is moving along the trajectory parallel to the time axis t'. because the x axis has to be perpendicular to the time axis of an object observed from the xt system i.e. to the axis of time t' 
The choice of x'axis of x't' coordinate system is equivalent to the statement saying that the point P is moving along the trajectory parallel to the time axis t. because the x' axis has to be perpendicular to the time axis of an object observed from the x't' system i.e. to the axis of time t 
Formulas of the Lorentz transformation have no physical meaning, because they are describing the observation of two separate bodies moving along two different trajectories and are true only in the point that is the intersection of these trajectories THE MOST IMPORTANT DIFFERENCE BETWEEN THE SRT AND THE FER IS THE FACT THAT, IN THE FER MODEL, IN ORDER TO DESCRIBE THE COORDINATES OF ANY BODY/POINT, IT IS NECESSARY TO KNOW THE TRAJECTORY OF THIS BODY/POINT, WHILE IN THE SRT THE KNOWLEDGE OF THE TRAJECTORY (WORLDLINE IN SRT) IS NOT NECESSARY 