$\overline{Y Z}$ is dilated by a scale factor of $\frac{1}{4}$ to form $\overline{Y^{\prime} Z^{\prime}} \cdot \overline{Y^{\prime} Z^{\prime}}$ measures 7 . What is the measure of $\overline{Y Z}$ ?

Step 1 ：Understand the problem. The problem is asking us to find the original length of a line segment after it has been reduced by a scale factor of \(\frac{1}{4}\).

Step 2 ：Set up the equation. If \(\overline{Y^\prime Z^\prime}\) is the result of dilating \(\overline{Y Z}\) by a scale factor of \(\frac{1}{4}\), then we can say that \(\overline{Y^\prime Z^\prime} = \frac{1}{4} \cdot \overline{Y Z}\).

Step 3 ：Substitute the given values into the equation. We know that \(\overline{Y^\prime Z^\prime}\) measures 7, so we can substitute this value into the equation to get \(7 = \frac{1}{4} \cdot \overline{Y Z}\).

Step 4 ：Solve for \(\overline{Y Z}\). To isolate \(\overline{Y Z}\), we can multiply both sides of the equation by 4 to get \(\overline{Y Z} = 4 \cdot 7\).

Step 5 ：Simplify the result. Multiplying 4 by 7 gives us 28, so \(\overline{Y Z} = 28\).

Step 6 ：Check the result. If we substitute \(\overline{Y Z} = 28\) back into the original equation, we get \(7 = \frac{1}{4} \cdot 28\), which simplifies to \(7 = 7\), confirming that our result is correct.

Step 7 ：Therefore, the measure of \(\overline{Y Z}\) is \(\boxed{28}\).