Question

suppose m is the midpoint of \\(\overline{fg}\\). find the missing measure. \\(fm = 5y + 13\\), \\(mg = 5 - 3y\\) \\(fg = \boxed{}\\) need help?

Explanation:

Step1: Use midpoint property

Since \( M \) is the midpoint of \( \overline{FG} \), \( FM = MG \). So set \( 5y + 13 = 5 - 3y \).

Step2: Solve for \( y \)

\( 5y + 3y = 5 - 13 \)
\( 8y = -8 \)
\( y = -1 \).

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

Substitute \( y = -1 \) into \( FM \): \( 5(-1) + 13 = -5 + 13 = 8 \).
\( MG \) is also \( 8 \) (since \( FM = MG \)).

Step4: Calculate \( FG \)

\( FG = FM + MG = 8 + 8 = 16 \).

Answer:

\( 16 \)