Question

△abc is the image of △abc after a dilation. the side lengths in centimeters of △abc are ab = 25, bc = 30, and ac = 10. the side lengths in centimeters of △abc are ab = 10, bc = 12, and ac = 4. what is the scale factor of the dilation? enter your answer as an improper fraction in simplest form by filling in the boxes. the scale factor is (\frac{square}{square}).

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ of a dilation is given by the ratio of the length of a side in the image to the length of the corresponding side in the pre - image. We can use any pair of corresponding sides. Let's use side $AB$ and $A'B'$.

Step2: Calculate the scale factor

$k=\frac{A'B'}{AB}$. Given $A'B' = 25$ and $AB = 10$, then $k=\frac{25}{10}=\frac{5}{2}$.

Answer:

$\frac{5}{2}$