Question

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?

Answer 1

let line length be \(l\). Then \(x\) and \(y\), such that \(|x|+|y|=l\) will be what you whant. Graphicly:

Answer 2

myko, could you please give more details? Thanks!

Answer 3

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.