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Puzzle in the squared notebook

In a squared notebook draw segments (0,10)-(0,0), (0,9)-(1,0), (0,8)-(2,0), ..., (0,0)-(10,0). (These are shown as segments AB in the figure below. Just drag point A to get the segments in red.) Can you determine the contour of the segments by setting up an equation? (We assume that you continue to draw the segments infinitely for all possible (0,t)-(10-t,0) segments where t runs between 0 and 10.)