Question

8 fill in the blank 1 point if g is the midpoint of \\(\overline{fh}\\), find fg. \\(11x - 7\\) \\(3x + 9\\) f g h fg = type your answer...

Explanation:

Step1: Set FG equal to GH (midpoint property)

Since \( G \) is the midpoint of \( \overline{FH} \), \( FG = GH \). So we set up the equation:
\( 11x - 7 = 3x + 9 \)

Step2: Solve for \( x \)

Subtract \( 3x \) from both sides:
\( 11x - 3x - 7 = 9 \)
\( 8x - 7 = 9 \)

Add 7 to both sides:
\( 8x = 9 + 7 \)
\( 8x = 16 \)

Divide both sides by 8:
\( x = \frac{16}{8} = 2 \)

Step3: Substitute \( x \) into FG's expression

The expression for \( FG \) is \( 11x - 7 \). Substitute \( x = 2 \):
\( FG = 11(2) - 7 \)
\( FG = 22 - 7 \)
\( FG = 15 \)

Answer:

15