Question

the segment below is the image of \\( \overline { e f } \\) after dilation by a scale factor of 4. what is the measure of \\( \overline { e f } \\)?

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 \(EF = x\), the scale factor \(k = 4\), and \(E'F=8\).

Step2: Solve for \(x\)

Using the formula \(E'F = k\times EF\), substitute the values: \(8 = 4\times x\). Then, solve for \(x\) by dividing both sides of the equation by \(4\): \(x=\frac{8}{4}=2\).

Answer:

\(2\)