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{err,transfo} = 
 FindGeometricTransform[list1, list2, 
  TransformationClass -> "Rigid"];

transfo = FindGeometricTransform[list1, list2, TransformationClassThen to visualize:

ListPlot[{list1,list2,transfo[list2],Joined->True]

enter image description here

Now... How do I get the displacment info in x and in y and the rotation info that was needed to do the geometric -> "Rigid"];

transfo = FindGeometricTransform[list1, list2, TransformationClass -> "Rigid"];

{err,transfo} = 
 FindGeometricTransform[list1, list2, 
  TransformationClass -> "Rigid"];

Then to visualize:

ListPlot[{list1,list2,transfo[list2],Joined->True]

enter image description here

Now... How do I get the displacment info in x and in y and the rotation info that was needed to do the geometric

2 added 150 characters in body
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EDIT:

Here are some starting hints based on comments:

transfo = FindGeometricTransform[list1, list2, TransformationClass -> "Rigid"];

EDIT:

Here are some starting hints based on comments:

transfo = FindGeometricTransform[list1, list2, TransformationClass -> "Rigid"];

1
source | link

Rotate and displace a line such that it fits another line

I have two lists:

list1 = {{0., 7.}, {-0.0701898, 7.01875}, {-0.140755, 7.03679}, {-0.211687, 
  7.05412}, {-0.28298, 7.07073}, {-0.354627, 7.08663}, {-0.426619, 
  7.10179}, {-0.498951, 7.11622}, {-0.571613, 7.12991}, {-0.644599, 
  7.14286}, {-0.717901, 7.15506}, {-0.791511, 7.16651}, {-0.865421, 
  7.1772}, {-0.939625, 7.18712}, {-1.01411, 7.19628}, {-1.08888, 
  7.20466}, {-1.16391, 7.21227}, {-1.23921, 7.21909}, {-1.31475, 
  7.22513}, {-1.39054, 7.23037}, {-1.46657, 7.23482}, {-1.54283, 
  7.23848}, {-1.6193, 7.24132}, {-1.69599, 7.24336}, {-1.77287, 
  7.24459}, {-1.84995, 7.24501}, {-1.92722, 7.2446}, {-2.00466, 
  7.24338}, {-2.08227, 7.24132}, {-2.16004, 7.23844}, {-2.23796, 
  7.23472}, {-2.31602, 7.23017}, {-2.39421, 7.22478}, {-2.47253, 
  7.21854}, {-2.55096, 7.21146}, {-2.62949, 7.20353}, {-2.70813, 
  7.19475}, {-2.78684, 7.18512}, {-2.86564, 7.17463}, {-2.9445, 
  7.16328}, {-3.02342, 7.15107}, {-3.10239, 7.13799}, {-3.1814, 
  7.12405}, {-3.26045, 7.10924}, {-3.33951, 7.09356}, {-3.41858, 
  7.07701}, {-3.49766, 7.05958}, {-3.57673, 7.04128}, {-3.65578, 
  7.0221}, {-3.73481, 7.00204}, {-3.8138, 6.98111}, {-3.89274, 
  6.95929}, {-3.97163, 6.93659}, {-4.05045, 6.913}, {-4.12919, 
  6.88854}, {-4.20785, 6.86318}, {-4.28642, 6.83694}, {-4.36488, 
  6.80982}, {-4.44322, 6.7818}, {-4.52144, 6.7529}, {-4.59953, 
  6.72311}, {-4.67747, 6.69244}, {-4.75526, 6.66087}, {-4.83288, 
  6.62842}, {-4.91033, 6.59508}, {-4.98759, 6.56085}, {-5.06466, 
  6.52574}, {-5.14152, 6.48973}, {-5.21817, 6.45285}, {-5.29459, 
  6.41507}, {-5.37078, 6.37641}, {-5.44672, 6.33687}, {-5.52241, 
  6.29645}, {-5.59784, 6.25514}, {-5.67298, 6.21295}, {-5.74785, 
  6.16989}, {-5.82241, 6.12595}, {-5.89668, 6.08113}, {-5.97062, 
  6.03544}, {-6.04425, 5.98887}, {-6.11753, 5.94144}, {-6.19047, 
  5.89313}, {-6.26306, 5.84396}, {-6.33528, 5.79393}, {-6.40712, 
  5.74304}, {-6.47858, 5.69129}, {-6.54964, 5.63868}, {-6.62029, 
  5.58522}, {-6.69053, 5.5309}, {-6.76035, 5.47574}, {-6.82973, 
  5.41974}, {-6.89866, 5.36289}, {-6.96714, 5.30521}, {-7.03515, 
  5.24669}, {-7.10269, 5.18734}, {-7.16974, 5.12717}, {-7.2363, 
  5.06617}, {-7.30235, 5.00435}, {-7.36789, 4.94172}, {-7.43291, 
  4.87827}, {-7.49739, 4.81402}, {-7.56133, 4.74896}, {-7.62471, 
  4.68311}, {-7.68753, 4.61646}, {-7.74978, 4.54902}, {-7.81145, 
  4.4808}, {-7.87253, 4.4118}, {-7.93301, 4.34203}, {-7.99287, 
  4.27148}, {-8.05212, 4.20017}, {-8.11074, 4.12811}, {-8.16872, 
  4.05529}, {-8.22606, 3.98172}, {-8.28273, 3.90741}, {-8.33875, 
  3.83236}, {-8.39409, 3.75659}, {-8.44874, 3.68009}, {-8.5027, 
  3.60287}, {-8.55597, 3.52494}, {-8.60852, 3.4463}, {-8.66035, 
  3.36697}, {-8.71145, 3.28694}, {-8.76182, 3.20622}, {-8.81145, 
  3.12483}, {-8.86032, 3.04276}, {-8.90843, 2.96003}, {-8.95576, 
  2.87664}, {-9.00232, 2.7926}, {-9.0481, 2.70792}, {-9.09307, 
  2.62259}, {-9.13725, 2.53664}, {-9.18061, 2.45007}, {-9.22315, 
  2.36288}, {-9.26487, 2.27509}, {-9.30574, 2.1867}, {-9.34578, 
  2.09771}, {-9.38497, 2.00815}, {-9.42329, 1.91801}, {-9.46075, 
  1.8273}, {-9.49734, 1.73604}, {-9.53305, 1.64423}, {-9.56786, 
  1.55188}, {-9.60179, 1.45899}, {-9.63481, 1.36558}, {-9.66691, 
  1.27166}, {-9.69811, 1.17723}, {-9.72838, 1.0823}, {-9.75771, 
  0.986886}, {-9.78611, 0.890993}, {-9.81357, 0.79463}, {-9.84008, 
  0.697808}, {-9.86563, 0.600534}, {-9.89021, 0.502819}, {-9.91383, 
  0.404672}, {-9.93647, 0.306104}, {-9.95813, 0.207122}, {-9.9788, 
  0.107739}, {-9.99848, 0.00796206}}

and:

list2 = {{0., 4.}, {-0.0403813, 4.038}, {-0.0815225, 4.07558}, {-0.123419, 
  4.11274}, {-0.166067, 4.14947}, {-0.209462, 4.18575}, {-0.253599, 
  4.22157}, {-0.298473, 4.25693}, {-0.344079, 4.29181}, {-0.390412, 
  4.32619}, {-0.437467, 4.36008}, {-0.485239, 4.39345}, {-0.533721, 
  4.4263}, {-0.582908, 4.45862}, {-0.632795, 4.49039}, {-0.683374, 
  4.52161}, {-0.734641, 4.55226}, {-0.786588, 4.58233}, {-0.83921, 
  4.61182}, {-0.892499, 4.6407}, {-0.94645, 4.66898}, {-1.00105, 
  4.69664}, {-1.05631, 4.72367}, {-1.1122, 4.75007}, {-1.16872, 
  4.77581}, {-1.22587, 4.80089}, {-1.28364, 4.82531}, {-1.34201, 
  4.84904}, {-1.40099, 4.87209}, {-1.46056, 4.89444}, {-1.52072, 
  4.91608}, {-1.58146, 4.937}, {-1.64276, 4.9572}, {-1.70463, 
  4.97666}, {-1.76705, 4.99538}, {-1.83001, 5.01334}, {-1.89351, 
  5.03054}, {-1.95753, 5.04696}, {-2.02207, 5.06261}, {-2.08712, 
  5.07746}, {-2.15266, 5.09152}, {-2.21869, 5.10477}, {-2.2852, 
  5.11721}, {-2.35218, 5.12882}, {-2.41962, 5.1396}, {-2.48751, 
  5.14954}, {-2.55584, 5.15864}, {-2.6246, 5.16688}, {-2.69377, 
  5.17425}, {-2.76336, 5.18076}, {-2.83334, 5.18639}, {-2.90371, 
  5.19113}, {-2.97445, 5.19499}, {-3.04556, 5.19794}, {-3.11703, 
  5.19999}, {-3.18883, 5.20112}, {-3.26097, 5.20134}, {-3.33344, 
  5.20062}, {-3.40621, 5.19898}, {-3.47928, 5.1964}, {-3.55264, 
  5.19287}, {-3.62627, 5.1884}, {-3.70016, 5.18296}, {-3.77431, 
  5.17657}, {-3.8487, 5.1692}, {-3.92331, 5.16087}, {-3.99814, 
  5.15155}, {-4.07318, 5.14125}, {-4.1484, 5.12996}, {-4.22381, 
  5.11768}, {-4.29938, 5.10441}, {-4.37511, 5.09013}, {-4.45098, 
  5.07484}, {-4.52697, 5.05854}, {-4.60309, 5.04122}, {-4.67931, 
  5.02289}, {-4.75562, 5.00353}, {-4.832, 4.98315}, {-4.90845, 
  4.96174}, {-4.98496, 4.93929}, {-5.0615, 4.91581}, {-5.13807, 
  4.89128}, {-5.21466, 4.86572}, {-5.29124, 4.83911}, {-5.36781, 
  4.81145}, {-5.44435, 4.78274}, {-5.52085, 4.75298}, {-5.5973, 
  4.72216}, {-5.67368, 4.69029}, {-5.74998, 4.65737}, {-5.82619, 
  4.62338}, {-5.90229, 4.58833}, {-5.97826, 4.55222}, {-6.05411, 
  4.51504}, {-6.1298, 4.47681}, {-6.20533, 4.4375}, {-6.28068, 
  4.39714}, {-6.35585, 4.3557}, {-6.43081, 4.31321}, {-6.50555, 
  4.26964}, {-6.58007, 4.22501}, {-6.65433, 4.17932}, {-6.72834, 
  4.13256}, {-6.80208, 4.08473}, {-6.87552, 4.03584}, {-6.94867, 
  3.98589}, {-7.0215, 3.93488}, {-7.09401, 3.88281}, {-7.16617, 
  3.82968}, {-7.23797, 3.7755}, {-7.30941, 3.72025}, {-7.38046, 
  3.66396}, {-7.45111, 3.60662}, {-7.52135, 3.54822}, {-7.59116, 
  3.48878}, {-7.66053, 3.4283}, {-7.72945, 3.36678}, {-7.7979, 
  3.30422}, {-7.86587, 3.24063}, {-7.93334, 3.17601}, {-8.00031, 
  3.11036}, {-8.06675, 3.04368}, {-8.13265, 2.97599}, {-8.19801, 
  2.90728}, {-8.2628, 2.83757}, {-8.32701, 2.76684}, {-8.39063, 
  2.69512}, {-8.45364, 2.62239}, {-8.51603, 2.54868}, {-8.57779, 
  2.47398}, {-8.63891, 2.3983}, {-8.69937, 2.32164}, {-8.75915, 
  2.24401}, {-8.81825, 2.16542}, {-8.87664, 2.08586}, {-8.93433, 
  2.00536}, {-8.99129, 1.92391}, {-9.04751, 1.84152}, {-9.10297, 
  1.7582}, {-9.15767, 1.67395}, {-9.2116, 1.58879}, {-9.26473, 
  1.50271}, {-9.31705, 1.41572}, {-9.36857, 1.32785}, {-9.41925, 
  1.23908}, {-9.46908, 1.14943}, {-9.51807, 1.0589}, {-9.56618, 
  0.967515}, {-9.61342, 0.87527}, {-9.65977, 0.782176}, {-9.70521, 
  0.688243}, {-9.74973, 0.593479}, {-9.79332, 0.497893}, {-9.83598, 
  0.401495}, {-9.87768, 0.304292}, {-9.91842, 0.206296}, {-9.95818, 
  0.107516}, {-9.99696, 0.00796084}}

Now I can plot them on a graph:

ListPlot[{list1,list2},Joined -> True]

enter image description here

Now the question is:

I would like to move the yellow line in such a way that it resembles as much as possible the blue line. I don't want to distort the line, just move it in x-y direction or rotate it.

In the end I would like to have a program that automatically figures out the best x and y mouvement and best rotation about a point (the program should also find that point and the angle) such that the the yellow line fits as good as possible above the blue line.

How can I do that ?