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New to Forum help with Projections

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Hello I am new to the Forum and am trying to find a way to apply a scale factor to a data set I want to bring into my project. Our
images are in NAD83 Feet, NM state plain central coordinate system. In the field our surveyors apply a grid to ground scale factor of 1.00xxxxxx to the NM grid coords. I would like to know how to assign a projection to these drawings when I add the data to our
ArcMap project our ground .dwg lines up with the state plain project. Can I just assign NM state plain central and change the scale factor or something else? Any help is appreciated I have tried searching the forums but am unclear.
Thanks

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