Question

question
\overline{uv} is dilated by a scale factor of 4 to form \overline{uv}. \overline{uv} measures 32. what is the measure of \overline{uv}?
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Explanation:

Step1: Recall dilation formula

When a segment is dilated by a scale factor \( k \), the length of the dilated segment \( L' \) is related to the original length \( L \) by \( L' = k \times L \). Here, the scale factor \( k = 4 \), the dilated length \( U'V' = 32 \), and we need to find the original length \( UV \).

Step2: Solve for original length

From \( L' = k \times L \), we can rearrange to find \( L=\frac{L'}{k} \). Substituting \( L' = 32 \) and \( k = 4 \), we get \( UV=\frac{32}{4} \).

Step3: Calculate the result

\( \frac{32}{4}=8 \).

Answer:

8