Question

suppose mis the midpoint of fg. find the missing measure. fm = 3n + 1, mg = 6 - 2n fg =

Explanation:

Step1: Use the midpoint property

Since \(M\) is the midpoint of \(\overline{FG}\), then \(FM = MG\).
So, \(3n + 1=6 - 2n\).

Step2: Solve for \(n\)

Add \(2n\) to both sides: \(3n+2n + 1=6-2n + 2n\), which simplifies to \(5n+1 = 6\).
Subtract \(1\) from both sides: \(5n+1-1=6 - 1\), so \(5n=5\).
Divide both sides by \(5\): \(n=\frac{5}{5}=1\).

Step3: Find \(FM\) and \(MG\)

Substitute \(n = 1\) into \(FM=3n + 1\): \(FM=3\times1+1=4\).
Substitute \(n = 1\) into \(MG=6 - 2n\): \(MG=6-2\times1 = 4\).

Step4: Calculate \(FG\)

Since \(FG=FM + MG\), then \(FG=4 + 4=8\).

Answer:

\(8\)