In an article that I am currently [reading](https://galileo.phys.virginia.edu/classes/252/lorentztrans.html) (under the Lorentz Invariants sub-heading), it explains that, just as the distance between two points on a Cartesian plane are obviously invariant of the coordinate system, the “spacetime distance” is also invariant. While in Cartesian coordinates $$(x\_1-x\_2)^2+(y\_1-y\_2)^2 = (x\_1'-x\_2')^2+ (y\_1'-y\_2')^2,$$ the space time analog is $$c^2(t\_1-t\_2)^2-(x\_1-x\_2)^2 = c^2(t\_1'-t\_2')^2- (x\_1'-x\_2')^2 = s^2$$ where $s^2$ is the spacetime interval.

I am having difficulty in understanding this notion of a spacetime interval and the intuition/derivation for why it can be written in this way and is invariant under Lorentz transformation.

I am aware that similar questions have been asked on this platform but none of them have fully cleared things up for me so far. Any help in providing an intuition or understanding would be appreciated.