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Your response to this problem requires extensive analysis of a coordinate dataset with 50 pairs of geographic and thematic data points. For the sake of understanding and explanation in providing you a solution in a required format which your system can execute. However, due to restrictions on output for execution or print operations as described, this answer is best suited to help users in solving their problem through logical thinking. First off we need an import for `itertools`, that helps use functions to make the solution run more quickly. ```python import itertools points1 = [ [0,-12.123456789], [-5.34321095,13.87654321], [8.987654321,-11.23456789] ] # Points for y coordinate line: pointsyline1=[16,-4.3237849] ``` Next we find points along a defined route and assign their corresponding coordinates as described. ```python def find_points_along_line(points,y_intercept,slope,endY,endX): # First define our interval between point starts based on how dense of detail needed to match reference dataset for accuracy. intervals=30 increment=endY/y_intercept/intervals results=[] # Create array to store each segment along line (we will fill this in next function linearray=[] # Find our interval, iterate over it to define segments for plotting. y=float(y_intercept)+increment x=slope*(y-y_intercept)+float(x[0]) points_at_intervals.append([x,y]) # Get every Nth data point def filter_N_data_point(inputlist,N): data=[] for num,element in enumerate( list(itertools.accumulate(inputlist))): if(num+1) %N== 0 : #if len(element)==2 and float ( element[0]) >100 and element == inputdata[len(inputdata)-3] and 'Hole' not in str( element): data.append(str(element)) return (str(data)) points_at_intervals=[] # Apply filter N to both X,Y data. points_along_x_axis=filter_N_data_point(points1[0],4) x = slope*(yfloat-endY)/(y_endy -y_start)-startx+startYend_start) points_at_y=interval results=[slope,x,increment] find_points_along_line([[14.545, -0.12356], [6.1235,-2.32356], [[14,9],[12.33,-6],13,-1]] ,7 , 6 ,11 ,-7) print( "results ", points_at_intervals) ``` As we understand, given an issue in question, a function find\_points along line is to use along data line for finding segments for a plot using point of a coordinate list for both Y coordinates. As seen this was created by adding lines as you have more intervals between the two ends. The solution has also a print out. Please keep following lines intact while making copy-pasting and do run the output by using Jupyter cell. To obtain more density with a similar route that doesn't show each point individually as before (with lower density). Please run to get better resolution. Hope you have enjoyed reading through how we approached it in our explanation to achieve an execution from question. I appreciate that we hope was very useful for our system readers.