Question

consider the original complex figure and the reduction.
what is the scale factor of the reduction?

Explanation:

Step1: Find the ratio of corresponding sides

The scale factor \(k\) is given by the formula \(k=\frac{\text{length of side in reduction}}{\text{length of corresponding side in original}}\). Here, a corresponding side in the original is \(32\) mm and in the reduction is \(4\) mm.
So, \(k = \frac{4}{32}\)

Step2: Simplify the ratio

Simplify \(\frac{4}{32}\) by dividing numerator and denominator by their greatest - common divisor, which is \(4\).
\(\frac{4\div4}{32\div4}=\frac{1}{8}\)

Answer:

\(\frac{1}{8}\)