Question

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what is the scale factor of the dilation? scale factor =

Explanation:

Step1: Find the length of a corresponding side in the original and dilated figure

In the original triangle \( \triangle ABC\), \(CB = 4\) (since \(B\) is at \(x = 4\) and \(C\) is at \(x=0\)). In the dilated triangle \( \triangle A'B'C\), \(CB'=8\) (since \(B'\) is at \(x = 8\) and \(C\) is at \(x = 0\)).

Step2: Calculate the scale factor

The formula for the scale factor \(k\) of a dilation is \(k=\frac{\text{length of side in image}}{\text{length of corresponding side in pre - image}}\). So \(k=\frac{CB'}{CB}\). Substituting the values, we get \(k=\frac{8}{4}\).

Answer:

\(2\)