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I have a Google earth image which has drawn polygons on it. I would like to create a polygon feature class in ArcGIS using this data. However, the actual image has been manipulated in powerpoint.

Is there a simple method to do this?

The image is a JPEG with 23 polygons drawn on it indicating different areas.

The process is not making much sense to me as the original image has no spatial reference aside from the Google Earth projection.

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You can load the ESRI Basemap Imagery and using the Georeferencing toolbar, georeference your jpeg image. If you zoom to your area of interest, the "Fit to Display" option will shift your image to the center of the map, making it easier to georeference. Once the image is rectified, create a feature class and digitize the 23 polygons.

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