July 1st, 2015, 08:33 PM  #1 
Newbie Joined: Jul 2015 From: US Posts: 2 Thanks: 0  Parallel line calculations???
I have a set of lines where I know the beginning and end coordinates (X1, Y1, X2, Y2). What I need to calculate is a set of begin/end coordinates for parallel lines that makes the line a set distance away. Example, if I have coordinates (0,0,50,0), which is a horizontal line, and the distance required is 10, then what I should end up with is (0,10,50,10) a line that is parallel to the first but offset by 10. I plan to put in +10 and 10 for the distances to get lines the same distance on either side. How would I go about that? 
July 2nd, 2015, 05:13 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
For nonhorizontal and nonvertical lines, the calculation is quite a lot more tedious. Suppose you have a line with one point $\displaystyle (x_0, y_0)$ and another point [math](x_1 , y_1)[math] (I would not say "end points" lines do not have ends). You need to find a line perpendicular to that line at each point. The given line has slope $\displaystyle \frac{y_1 y_0}{x_1 x_0}$. Any line perpendicular to that given line must have slope $\displaystyle \frac{x_0 x_1}{y_1 y_0}$. A line through $\displaystyle (x_0, y_0)$ perpendicular to that given line has equation $\displaystyle y= \left(\frac{x_0 x_1}{y_1 y_0}\right)(x x_0)+ y_0$. Now you will have to use the distance formula to find a point on this new line at the desired distance from $\displaystyle (x_0, y_0)$. Do the same with point $\displaystyle (x_1, y_1)$.


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calculations, line, parallel 
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