Question

polygon p is a scale copy of polygon n. what scale factor takes polygon n to polygon p?

Explanation:

Step1: Identify corresponding sides

Take a pair of corresponding sides. For example, the side of length \(4\) in polygon \(N\) and the side of length \(10\) in polygon \(P\).

Step2: Calculate scale factor

The formula for scale factor \(k\) is \(k=\frac{\text{length of side in image (polygon }P\text{)}}{\text{length of side in original (polygon }N\text{)}}\). So \(k = \frac{10}{4}=\frac{5}{2}= 2.5\).
Another check: Using side \(16\) in \(N\) and \(40\) in \(P\), \(k=\frac{40}{16}=\frac{5}{2} = 2.5\). Using side \(8\) in \(N\) and \(20\) in \(P\), \(k=\frac{20}{8}=\frac{5}{2}=2.5\).

Answer:

\(2.5\)