Question

1. if g is the midpoint of $overline{fh}$, find $fg$.

$11x - 7$ quad $3x + 9$
$f$ quadquadquad $g$ quadquadquad $h$

Explanation:

Step1: Use 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 by 8: \( x = \frac{16}{8} = 2 \)

Step3: Find FG

Substitute \( x = 2 \) into \( FG = 11x - 7 \):
\( FG = 11(2) - 7 = 22 - 7 = 15 \)

Answer:

15