How to reorient multiple lines to a specific bearing

I am dealing with river cross-section survey data, repeated at the same locations on a number of occasions over time. The surveyors started and ended each section at the same locations, but did not always follow a straight line, or the same zig-zag line. I want to project all the surveyed points to a straight line between the end points, so I am comparing sections of identical length. In GM I can first create a straight line between the end points. Then I can create a (non-straight) line from the surveyed points, create perpendicular lines at each vertex, then rotate the lines to be perpendicular to the straight line between the end points. The lines would all be aligned at the same bearing (perpendicular to the bearing of the straight line between end points). Then I can assign the elevations of the surveyed points to the lines they are associated with, grid the lines, then draw a profile along the straight line between the end points. This is a long manual process, not feasible considering how much data I have. I would like to be able to automatically do the step of reorienting all the created perpendicular lines at the surveyed point to be perpendicular to the straight line between end points. I know the bearing of that line, so the specified bearing is orthogonal to that. The lines should all rotate about their centres (i.e. the surveyed points). My understanding is that at present the rotate function can only rotate BY a specific angle, not TO a specific bearing, and cannot rotate multiple lines about their centres.
Best Answers
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Maybe this will help, If I understood correctly this is what I would do:
Select the end points line and the surveyed points and use Move Selected Points to Nearest Line.
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That's a brilliant solution. You have saved me a lot of time and effort.
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