Question

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

Explanation:

Step1: Use the midpoint 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 \(FG = 2MG\) to get \(15=2(13x + 1)\).

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 simplifies to \(13 = 26x\). Then divide both sides by \(26\): \(x=\frac{13}{26}\).

Answer:

\(x = \frac{1}{2}\)