Question

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

Explanation:

Step1: Use mid - point property

Since \(M\) is the midpoint of \(\overline{FG}\), then \(FG = 2MG\).

Step2: Substitute the given expressions

Given \(MG=13x + 1\) and \(FG = 15\), we substitute into \(FG = 2MG\):
\(15=2(13x + 1)\)

Step3: Expand the right - hand side

Using the distributive property \(a(b + c)=ab+ac\), we have \(15 = 26x+2\).

Step4: Solve for \(x\)

Subtract \(2\) from both sides: \(15−2=26x+2−2\), which gives \(13 = 26x\).
Then divide both sides by \(26\): \(x=\frac{13}{26}\).
Simplify \(\frac{13}{26}\) to \(x = 0.5\).

Answer:

\(x = 0.5\)