This demonstration uses the Lorentz transformation to calculate $(t^\prime,x^\prime)$, the coordinates of an event in the moving frame of reference, as well as the spacetime distance between the event and the origin in both the stationary and moving frames. Use the first two sliders to pick the $(t,x)$ coordinates of an event in the stationary frame and the third slider to pick the speed of the moving frame. While coordinate values change as you change the speed $v$, the spacetime distance (interval) between the event and the origin stays fixed. You can see this explicitly in the final line of the demonstration. For a fixed choice of $(t,x)$, when you change the value of $v$ (third slider), notice that the right hand side of the spacetime interval calculation stays fixed.
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