Trying to understand your question, perhaps this picture might help.
You seem to be asking how to find out whether the point $C$ is inside the thick line $AB$.
You should drop a perpendicular from $C$ to $AB$, meeting at the point $D$. If the (absolute) length of $CD$ is more than half the width of the thick line then $C$ is outside the thick line (as shown in this particular case).
If the thick line is in fact a thick segment, then you also have to consider whether $D$ is between $A$ and $B$ (or perhaps slightly beyond one of them, if the thickness extends further).