Question

$\triangle xyz$ is the image of $\triangle xyz$ under a dilation through point c. $xz = 16$ and $xz = 40$. what scale factor was used in the dilation?

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k\) of a dilation is given by \(k=\frac{\text{length of image segment}}{\text{length of pre - image segment}}\).

Step2: Substitute the given values

We are given that the length of the pre - image segment \(XZ = 16\) and the length of the image segment \(X'Z'=40\).
Substituting into the formula \(k=\frac{X'Z'}{XZ}\), we get \(k=\frac{40}{16}\).

Step3: Simplify the fraction

\(\frac{40}{16}=\frac{40\div8}{16\div8}=\frac{5}{2}=2.5\)

Answer:

\(2.5\)