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The set for a school play needs a replica of a historic building painted on a backdrop that is 24 feet long and 14 feet high. The actual building measures 432 feet long by 252 feet high. A stage crewmember writes 

(x, y)  →(1/22x, 1/22y) to represent the dilation. Is the crewmember's calculation correct if the painted replica is to cover the entire backdrop? Complete the explanation.

 

The stage crewmember's calculation is ______. The scale factor for the backdrop is 1/? .