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I have an assortment of coordinates for work, but they're split between two groups that aren't in reference to one another because I had to move my measurement tool partway through the survey. Because they're out of reference with one another, I have to manipulate them so that they cohere again. Fortunately, I have a common point that I measured between both groups and I know that they both trend in more or less the same direction. Therefore, I should be able to line the second group up with the first around this common point and then use the differences in trend to rotate the rest of the points such that they all follow the same line of best fit.

My plan was to use the line of best fit from the straight part of each line (the first line has a curve near the bottom) to generate right triangles and solves for the angle difference between them and then rotate line 2's coordinates by that amount (37.63 degrees) so things are all in a line with the line of best fit from line 1. However, my attempts at using X=xcos(θ)+ysin(θ), Y=−xsin(θ)+ycos(θ) have thus far not given me the results I'm looking for, with the second line always being at some strange angle. I won't post the whole excel sheet, but the steps I'm using are as follows - calculate cumulative incremental change from common point for each point of line 2. Excel will solve

=((O103\*COS(DEGREES(-37.36)))+(P103*SIN(DEGREES((-37.36)))))

for the easting or

=(-(O102\*SIN(DEGREES(-37.36)))+(P102*COS(DEGREES((-37.36)))))

for the northing, and then I'll add these new numbers back to the common point. This gets me numbers which aren't completely ridiculous - I think I am successfully doing some sort of rotation - but they also aren't right. Does anyone have any idea either what I'm doing wrong or how I could troubleshoot the issue? Thanks in advance!

I'll include the coordinates below if anyone wants to try this themselves - line of 100 is line 1 and the line at intervals of 10 is line 2, with the point marked "common" being the the point in line 2 that I measured relative to line 1.





Number|Easting|Northing
---|---|----
1|992.275|954.729
2|992.265|955.636
3|992.23|956.538
4|992.309|957.41
5|992.325|958.362
6|992.386|959.248
7|992.429|960.12
8|992.434|961.068
9|992.513|961.988
10|992.495|962.897
11|992.555|963.86
12|992.661|964.697
13|992.713|965.609
14|992.757|966.527
15|992.739|967.486
16|992.896|968.393
17|992.962|969.294
18|992.956|970.147
19|993.048|971.1
20|993.106|972.036
21|993.134|972.971
22|993.139|973.862
23|993.179|974.778
24|993.259|975.698
25|993.326|976.602
26|993.479|977.525
27|993.527|978.407
28|993.582|979.319
29|993.628|980.212
30|993.682|981.126
31|993.75|982.075
32|993.726|982.99
33|993.856|983.866
34|993.826|984.772
35|993.963|985.75
36|994.015|986.654
37|994.054|987.585
38|994.22|988.437
39|994.309|989.427
40|994.328|990.331
41|994.461|991.187
42|994.563|992.119
43|994.603|993.051
44|994.678|993.938
45|994.787|994.885
46|994.872|995.754
47|994.968|996.677
48|995|997.493
49|995.067|998.549
50|995.135|999.421
51|995.288|1000.303
52|995.321|1001.206
53|995.37|1002.058
54|995.526|1002.965
55|995.592|1003.841
56|995.683|1004.781
57|995.796|1005.666
58|995.853|1006.585
59|995.898|1007.525
60|996.008|1008.385
61|996.164|1009.321
62|996.212|1010.24
63|996.332|1011.154
64|996.382|1012.006
65|996.426|1012.959
66|996.491|1013.858
67|996.72|1014.793
68|996.747|1015.695
69|996.856|1016.636
70|996.976|1017.536
71|997.028|1018.436
72|997.174|1019.332
73|997.198|1020.278
74|997.258|1021.254
75|997.362|1022.159
76|997.463|1023.112
77|997.629|1023.985
78|997.708|1024.912
79|997.804|1025.849
80|997.835|1026.754
81|998.011|1027.66
82|998.138|1028.574
83|998.283|1029.453
84|998.363|1030.374
85|998.331|1031.354
86|998.479|1032.201
87|998.62|1033.185
88|998.765|1033.992
89|998.772|1034.913
90|998.982|1036.756
91|999.104|1037.667
92|999.266|1038.584
93|999.377|1039.467
94|999.42|1040.346
95|999.52|1041.291
96|999.606|1042.229
97|999.633|1043.123
98|999.721|1044.031
99|999.792|1044.936
common|1003.598|1076.377
1|1010.532|1003.99
10|1008.671|1001.956
20|1006.501|999.751
30|1004.402|997.517
40|1002.421|995.345
50|1000.327|993.077
60|998.26|990.901
70|996.249|988.785
80|994.2|986.563
90|991.968|984.418
100|989.981|982.218

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