plotting points on a graph at equal distances

I have a connected weighted graph with multiple edges.Traversing as in a euler tour, I have to partition the edges into equal intervals and get the x and y coordinates of these points on the graph. Interval length is fixed and given. Using the euler tour, i am trying to plot the points on the edges, but i am unable to get the coordinates correctly on the graph. I am using while loop and plot function but i am unable to adjust many conditions inside the loop. Can anyone please give some suggestions?

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