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Is there anyway that I can input:

  1. The Coordinates System (projected is OK)
  2. The bounding box

and create a rectangle polygon based on these?

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up vote 11 down vote accepted

I assume you have points/a polygon associated with your coordinate system. Try using Arc's Minimum Bounding Geometry (Data Management). Then select the "Envelope" or "Rectangle by Area/Width" geometry type.

enter image description here

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