Question

point f is on line segment \\( \overline{eg} \\). given \\( ef = 5 \\) and \\( fg = 3 \\), determine the length \\( \overline{eg} \\).

Explanation:

Step1: Analyze the relationship between line segments

Since point \(F\) is on line segment \(\overline{EG}\), we know that \(EG = EF+FG\) (by the segment addition postulate).

Step2: Substitute the given values

We are given \(EF = 5\) and \(FG=3\). Substituting these values into the formula \(EG = EF + FG\), we get \(EG=5 + 3\).

Step3: Calculate the result

\(5+3=8\).

Answer:

\(8\)