I've been trying to find out how to compute the corresponding point on the line $x=1$, starting from point $(95,30)$ knowing the normalized direction vector $(-0.9734,0.2290)$.
My idea is to compute at which point the "projection" of my normalized direction vector intersects on line $x=1$, but I fail every time since I think I ignore too much.
I think this is super basic trigonometry but if someone could point me out where can I read about it, it would be perfect!
It sounds like what you want to do is make a line from $(95,30)$ in the desired direction and find where it intersects the line $x=1$. This point of intersection if found by setting the line equations equal, plug in $x=1$ and solve for $y$.