Lorentz transformation on a space-time diagram. The transformation looks like a rotation of the axes except that the time and space axes rotate in opposite directions.

Invariance of lengths under rotation.The dark line represents the distance between points A and B.The components of this length with respect to the x- and y-axes are Ax and Ay, respectively, and with respect to the x'- and y'-axes are Ax' and Ay', respectively. Independent of the components used, the length of the dark line is the same.

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