Lorentz Transformation — two frames and an event

Drag the event P (in S). Slide β = v/c to boost. Top: the overlay view — one shared origin, S′ axes tilt toward the 45° light line, skew read-off. Bottom: S and S′ drawn separately, each with its own axes. Drag any origin dot to reposition.

ct0
x0
ct′0
x′0
0

s² = (ct)²−x² is the same in both frames.