Question

1. a developer wants to reduce this floor plan drawing so that it will fit on a brochure with other designs. the developer creates a scale in which 1 inch in the original floor plan drawing represents 0.5 inches in the reduced floor plan drawing.

a. what are the lengths in the reduced floor plan drawing?
b. what scale factor reduces the original floor plan drawing to the reduced floor plan drawing?

Explanation:

Step1: Find lengths in reduced drawing

The scale is 1 inch in original represents 0.5 inches in reduced. The original lengths are 6 inches and 3 inches. Multiply original lengths by scale - factor.
For the 6 - inch length: $6\times0.5 = 3$ inches.
For the 3 - inch length: $3\times0.5 = 1.5$ inches.

Step2: Calculate scale factor

The scale factor is the ratio of the length in the reduced drawing to the length in the original drawing. Since 1 inch in original becomes 0.5 inches in reduced, the scale factor is $\frac{0.5}{1}=0.5$.

Answer:

a. The lengths in the reduced floor - plan drawing are 3 inches and 1.5 inches.
b. The scale factor is 0.5.