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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

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    I edited your question. Check if this is what you would like to ask. Especially I think what you meant by "angle" is "slope".2011-12-24
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    First problem: take two points on the line, and consider the triangle formed by those two points and the given point. Compute the signed area. Check the sign to see if the point is on the line's left or right.2011-12-24
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    Please elaborate your question 2 so that I can understand it. There seems to be too many things happening.2011-12-24
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    Your figure doesn't quite tell anything. According to you, you have a line $L_1$ and a point $P$ associated with it. You shift and rotate the point and line together to a new location. Is this right?2011-12-24

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