Question

finding a scale factor you receive wallet - sized photos of your school picture. the photo is 2.5 inches by 3.5 inches. you ask the photographer to dilate the photo to 5 inches by 7 inches. what is the scale factor of this dilation?

Explanation:

Step1: Recall the formula for scale factor

Scale factor \(k=\frac{\text{dimension of dilated figure}}{\text{dimension of original figure}}\)

Step2: Calculate the scale factor using length

Original length \(l_1 = 3.5\) inches, dilated length \(l_2=7\) inches. Then \(k=\frac{l_2}{l_1}=\frac{7}{3.5}\)

$$ \frac{7}{3.5}=\frac{7\times2}{3.5\times 2}=\frac{14}{7} = 2 $$

Step3: Verify using width

Original width \(w_1 = 2.5\) inches, dilated width \(w_2 = 5\) inches. Then \(k=\frac{w_2}{w_1}=\frac{5}{2.5}\)

$$ \frac{5}{2.5}=\frac{5\times2}{2.5\times2}=\frac{10}{5}=2 $$

Answer:

\(2\)