YOU SAID:
The dog sat on its rug beside the fire
INTO JAPANESE
犬は火のそばの敷物の上に座っていました
BACK INTO ENGLISH
The dog was sitting on the rug by the fire
INTO JAPANESE
犬は火のそばで敷物の上に座っていました
BACK INTO ENGLISH
The dog was sitting on the rug by the fire
That didn't even make that much sense in English.