Question

the segment below is the image of $\overline{wx}$ after dilation by a scale factor of $\frac{1}{3}$. what is the measure of $\overline{wx}$?
$w$ 9 $x$

Explanation:

Step1: Recall the dilation formula

If a segment \(AB\) is dilated by a scale factor \(k\) to get \(A'B'\), then \(A'B'=k\times AB\). Here, let \(AB = \overline{WX}\), \(A'B'=\overline{W'X'}=9\), and \(k = \frac{1}{3}\).

Step2: Solve for the original segment length

We know that \(\overline{W'X'}=\frac{1}{3}\times\overline{WX}\). To find \(\overline{WX}\), we can rewrite the formula as \(\overline{WX}=\frac{\overline{W'X'}}{k}\). Substitute \(\overline{W'X'}=9\) and \(k=\frac{1}{3}\) into the formula. Then \(\overline{WX}=\frac{9}{\frac{1}{3}}\).

Step3: Calculate the value

Using the rule of dividing by a fraction (\(a\div\frac{b}{c}=a\times\frac{c}{b}\)), we have \(\overline{WX}=9\times3 = 27\).

Answer:

$27$