I have two problems I will be very grateful if somebody helps me about them. If I have a line $L_1$ with a known point $(x_1, y_1)$ on it and has slope $\theta_1$, how do I know if a point $P=(x, y)$ is right to it or left? Or upper or lower?
The second problem, if I get the distance between the previous point $P$ and the previous line $L_1$ as $d = \sqrt{(x-x_1)^2 + (y-y_1)^2}$, how can I relocate $P$ to a different line $L_2$ with a known point $(x_2, y_2)$ on it and has slope $\theta_2$ keeping the same distance between the new point and $L_2$, so what's the new $(x, y)$ for point $P$?
I don't have much experience in Vectors and any help will be much appreciated.
Many thanks,
Thank you guys for the help, I have attached an image to clarify my second problem. I want to get the red point location which should be located at the same distance and side and angle to L2. It's more like transferring L1 and P to another location as if P is attached to the line and transferred with it. I know my terms is not scientific at all but I will try my best to understand. Many thanks again. http://i.stack.imgur.com/15Ja1.jpg