Question

polygon k is a scaled copy of polygon j.
12.9
8.6
25.8
17.2
9.75
polygon j
polygon k
what scale factor takes polygon j to polygon k?

Explanation:

Step1: Find the scale factor

The scale factor \(k\) can be found by dividing the corresponding side lengths of the scaled - copy (polygon \(K\)) and the original polygon (polygon \(J\)). We can use the vertical sides. Let the side length of polygon \(J\) be \(a = 17.2\) and the side length of polygon \(K\) be \(b=25.8\).
The formula for the scale factor \(k=\frac{\text{side length of }K}{\text{side length of }J}\)
So, \(k = \frac{25.8}{17.2}\)

Step2: Simplify the fraction

\(\frac{25.8}{17.2}=\frac{25.8\div8.6}{17.2\div8.6}\) (dividing numerator and denominator by the greatest common divisor of \(25.8\) and \(17.2\), which is \(8.6\))
\(\frac{25.8\div8.6}{17.2\div8.6}=\frac{3}{2}=1.5\)

Answer:

The scale factor is \(1.5\)