Question

what scale factor takes polygon c to polygon d? polygon d is a scaled copy of polygon c. polygon c 12 20 44 polygon d 12\frac{1}{2} 7\frac{1}{2} 27\frac{1}{2}

Explanation:

Step1: Convert mixed numbers to improper fractions

For the side of polygon \(D\): \(12\frac{1}{2}=\frac{12\times2 + 1}{2}=\frac{25}{2}\), \(7\frac{1}{2}=\frac{7\times2+1}{2}=\frac{15}{2}\), \(27\frac{1}{2}=\frac{27\times 2+1}{2}=\frac{55}{2}\). For the side of polygon \(C\): \(20\), \(12\), \(44\).

Step2: Calculate the scale factor

The scale factor \(k\) from polygon \(C\) to polygon \(D\) is given by the ratio of corresponding side lengths. Let's take the side lengths \(20\) (polygon \(C\)) and \(12\frac{1}{2}=\frac{25}{2}\) (polygon \(D\)). The scale factor \(k=\frac{\text{side of }D}{\text{side of }C}\). So \(k = \frac{\frac{25}{2}}{20}=\frac{25}{2}\times\frac{1}{20}=\frac{25}{40}=\frac{5}{8}\). We can check with another pair of sides: \(\frac{\frac{15}{2}}{12}=\frac{15}{2}\times\frac{1}{12}=\frac{15}{24}=\frac{5}{8}\), and \(\frac{\frac{55}{2}}{44}=\frac{55}{2}\times\frac{1}{44}=\frac{55}{88}=\frac{5}{8}\)

Answer:

The scale factor is \(\frac{5}{8}\)