No, you draw lines according to conditions: $x=1+ct$, $x=-1+ct$, $x=1-ct$ and $x=-1-ct$.

And normally one need to consider all 9 domains. However, our problems have two symmetries and it is sufficient to consider only 4 domains intersecting with the 1st quadrant and extend solution to the remaining 5, using the fact that solution is either odd or even with respect to $t$ (you need to understand, what is the case), and also solution is either odd or even with respect to $x$ (you need to understand, what is the case).