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The Sol system is ~26,000 light years from the center of the galaxy. The UFP is about 8000 light years distant according to Picard in First Contact. So the Delta quadrant would be ~9 times the distance that this maps shows away in the direction of the Romulans (Kathy and crew have to travel 70000 light years). That's my best guess as I can't find a reliable quadrant map.