Question

ppose m is the midpoint of \\( \overline { f g } \\). find the missing measure.
\\( g = 13 x + 1, f g = 15 \\)

Explanation:

Step1: Use the mid - point property

Since \(M\) is the midpoint of \(\overline{FG}\), then \(MG=\frac{1}{2}FG\).
Given \(MG = 13x+1\) and \(FG = 15\), we substitute into the equation: \(13x + 1=\frac{1}{2}\times15\).

Step2: Solve the equation for \(x\)

First, simplify the right - hand side of the equation: \(\frac{1}{2}\times15=\frac{15}{2}=7.5\).
So the equation becomes \(13x+1 = 7.5\).
Subtract \(1\) from both sides: \(13x=7.5 - 1\).
\(13x=6.5\).
Divide both sides by \(13\): \(x=\frac{6.5}{13}\).
\(x = 0.5\).

Answer:

\(x = 0.5\)