Question

kary measured \\(\overline{fg}\\) and determined that m is the midpoint. how long is \\(\overline{fg}\\)?
f \\( 3x \\) m \\( 5x - 6 \\) g
a. \\( \bigcirc \\ fg = 18 \\)
b. \\( \bigcirc \\ fg = 9 \\)
c. \\( \bigcirc \\ fg = 12 \\)
d. \\( \bigcirc \\ fg = 3 \\)

Explanation:

Step1: Use midpoint property

Since M is the midpoint of \( \overline{FG} \), \( FM = MG \). So \( 3x = 5x - 6 \).

Step2: Solve for x

Subtract \( 3x \) from both sides: \( 0 = 2x - 6 \). Add 6 to both sides: \( 2x = 6 \). Divide by 2: \( x = 3 \).

Step3: Find length of FG

\( FG = FM + MG = 3x + (5x - 6) = 8x - 6 \). Substitute \( x = 3 \): \( 8(3) - 6 = 24 - 6 = 18 \).

Answer:

A. \( FG = 18 \)