Special Relativity, Light cones in Minkowski Diagrams

[king vitamin]

Homework Statement

Show that a point Q outside the "light cone" can occur either before or after a point P inside the light cone (eg: at the origin), depending upon the frame of reference. Show that a point R inside the light cone is always in the future or in the past with respect to P, irrespective of frame S'.

Homework Equations

this is just diagrams

The Attempt at a Solution

I know this isn't a difficult problem, but I'm having trouble conceptualizing it because I've never even seen light cones displaced from the origin, let alone in other frames of reference. How does a light cone transform between reference frames? I can't picture it because the x' and ct' axes are no longer orthogonal when drawn over S, so I'm not sure how to represent things.

 

[tiny-tim]

Hi king vitamin!

Forget the shape of the cone …

the question is just asking you to prove that x² > c²t², then in some frames t' > 0 but in others t' < 0 (while if x² < c²t², then in all frames, t' has the same sign).