For this problem, assume that any two frames have the same origin.Consider two events with coordinates $($t$1,$ x$1)$ and $($t$2,$ x$2)$ in an inertial frame of reference S$.$ The coordinates of these two events in an inertial frame S'moving to the right with speed u relative to frame S are $($t$\text{'},$ x$\text{'})$ and $($t$\text{'}2,$ X$\text{'},).$If we assume that the y and z coordinates are constant in the two frames, then x$\text{'},$ x$\text{'},$ is the space interval, more commonly known as distance, between the events as measured in frame S$\text{'},$ and x$2$ x$1$ is the space interval in the frameS. These two intervals are more commonly written