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Is there any known way to construct an infinite number of Cartesian coordinates (x and y pairs) for any given [line] length where every single abscissa (x coordinate) and ordinate (y coordinate) pair sum to the given [line] length?

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let line length be \(l\). Then \(x\) and \(y\), such that \(|x|+|y|=l\) will be what you whant. Graphicly: |dw:1364806664458:dw|
myko, could you please give more details? Thanks!
I am not completely sure about the question you are asking but it seems that all you need is to be given a line length, say "L" and then plot x + y = L from any starting point for the the to the length L. To construct this the x and y intercepts for an infinite line would be x = L and y = L. then any line segment of length L on that line would have infinite (x, y) coordinates that would add up to the line segment length L. There would be infinite line segments of length L on the line with those intercepts. |dw:1364826547833:dw|

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