Question

practice b: (first taught in lesson 8) in \\( \overline { f l } \\), \\( f g = 5 \\), \\( j l = 4 \\), and \\( f l = 12 \\). what is the distance from \\( f \\) to the midpoint of \\( \overline { g j } \\)?

Explanation:

Step1: Find the length of \( GJ \)

By the segment - addition postulate \( FL=FG + GJ+JL \).
We know \( FL = 12\), \(FG = 5\), and \(JL = 4\).
Substitute the values into the equation: \(12=5 + GJ+4\).
Simplify the right - hand side: \(12=9 + GJ\).
Solve for \(GJ\): \(GJ=FL-(FG + JL)=12-(5 + 4)=3\).

Step2: Find the mid - point of \( GJ \)

Let \(M\) be the mid - point of \(GJ\). Then \(GM=\frac{1}{2}GJ\).
Since \(GJ = 3\), \(GM=\frac{3}{2}=1.5\).

Step3: Find the distance from \(F\) to the mid - point of \(GJ\)

The distance \(FM=FG + GM\).
We know \(FG = 5\) and \(GM = 1.5\).
So \(FM=5+1.5 = 6.5\).

Answer:

\(6.5\)