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\\( \overline { w x } \\) is dilated by a scale factor of \\( \frac { 1 } { 4 } \\) to form \\( \overline { w ^ { \prime } x ^ { \prime } } \\). \\( w ^ { \prime } x ^ { \prime } \\) measures 9. what is
the measure of \\( \overline { w x } \\)?
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Explanation:

Step1: Recall the dilation formula

If a segment \(AB\) is dilated by a scale factor \(k\) to form \(A'B'\), then \(A'B'=k\times AB\). Here, let \(WX = x\), scale factor \(k=\frac{1}{4}\), and \(W'X' = 9\). So the equation is \(9=\frac{1}{4}\times x\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(9=\frac{1}{4}\times x\) by \(4\). Using the property of equality \(4\times9 = 4\times\frac{1}{4}\times x\). Since \(4\times\frac{1}{4}=1\), we get \(x = 36\).

Answer:

\(36\)