Lorentz transformation, time dilation, length contraction and Doppler Effect - all at once

We present a simple derivation of the Lorentz transformations for the space-time coordinates of the same event. It is based on the relative character of length and time interval as measured by observes in relative motion. We begin by accepting that the relative motion modifies in some particular way the result of these measurements. However we do not postulate the character of this distortion i.e. whatever it is dilation or contraction. The formulas accounting for length contraction, time dilation and Doppler shift are a byproduct of this derivation.