Length Shortening in STR

Einstein's light clock (system S) is supposed to fly past me (system B). The distance between the mirrors is ct. The light beam has just reached the lower plate. In system S, before time t, the photons left the upper point. This point, in system S and with a velocity v, was at a distance vt from me. I see the light beam coming from somewhere parallel to the perpendicular ct. The clock is supposed to have been at a distance x from me there, as seen from me. For x, the clock takes the same time as the light seen. According to Pythagoras, (ct´)² = x² + (ct)². With x = vt´, t´²(c²-v²) = c²t². Therefore, t´ is stretched relative to t by f = 1/sqrt(1-v²)), the Lorentz factor. Strangely, the path x = v·t·f also appears longer to me, not shortened. Where is the error? Is there a shortening of length?

A kite flies past me at speed v. At time 0, I see its head, and after time t, the tip of its tail. However, for the kite, time t has been extended by the Lorentz factor. Accordingly, its length is greater than the length I measured. So, the shortening of length exists. Where, then, is the (supposed) error in the initial example?
In the "speed of light" example, two spaceships move past me at a distance of one light-second. If their temporal separation is one second from me, the more distant ship sends a beam of light to its partner. There, it sees me at a distance vt. However, I see the light coming from a great distance. The spaceship therefore sees my length shortened. The point from which I see the light coming has nothing to do with the moving system, as one mistakenly assumes.

Einstein's Light Clock.

Ludwig Resch