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I have few question for deriving the Lorentz transformation (LT):

While deriving the LT, we draw a graph as x,y,z in one frame of reference and x',y',z' in the other frame of reference as S and S' as two frames of reference.

Now the factor ct comes in, which is the flash of light. Now we do:

x^2+y^2+z^2=c^2t^2.

(1) The ct factor is speed of light multiplied by time as ct, right?

(2) the square factor of x^2+y^2........How do we calculate? Are we using Pythagoras' theorem in this case?