Question

The set for a school play needs a replica of a historic building painted on a backdrop that is 20 feet long and 16 feet high. The actual building measures 320 feet long by 256 feet high. A stage crewmember writes (x, y) arrow right ( 1/20 x, 1/20y) to represent the dilation. Is the crewmember's calculation correct if the painted replica is to cover the entire backdrop? Complete the explanation.

Answer 1

Stage crewmember's calculation is incorrect

Correct = 1/16x 1/16y

Explanation:

Given that:

Dimension of backdrop : 20 feets long ; 16 feets high

Actual dimension of building : 320 feets long ; 256 feets high

The correct scale factor can be obtained thus :

Ratio of backdrop dimension to the actual dimension of building

Length : 20 / 320 = 1 /16

Height : 16 / 256 = 1/16

Hence, stage crewmember's calculation of (1/20x ; 1/20y) is incorrect.