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I have taken a JPEG image snapshot of an area on google earth. Within it I marked and record the coordinates of the four corners. I then added and georeferenced the image to a map I was already working in. However, the layers in my map are all NAD83. The Google earth image does not line up correctly. I want it to line up correctly with my other layers as I need to draw a new polygon using it.

How can I make the google earth image match my other layers?

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I think that you probably want to georeference your screenshot before applying any reprojections or transformations (since your screenshot has no coordinate system in its raw state). I would suggest opening a new ArcMap document, setting your Data Frame coordinate system to Plate Carree (Projections - World - WGS 1984 Plate Carree), and then bringing in the NAD83 layers from your original map. Your original layers will reproject on-the-fly to your new Data Frame CS, and you can then georeference your screenshot in the projection it was originally captured in. Once it is georeferenced, you can then project it to the same CS as you other data (if needed).

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    Yes, this is the way to go, though you may as well set it to WGS 1984 Web Mercator (Aux Sphere). Also, if it's an area with significant elevation variation, I'd set the elevation factor in google earth as low as possible before making the screenshot. GE has a kind-of "fish-eye" way of visualizing elevation, which will cause distortion in this operation.
    – mr.adam
    Commented Jun 2, 2015 at 21:31

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