Question

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

f 11x - 7 g 3x + 9 h

Explanation:

Step1: Set up equation using mid - point property

Since G is the midpoint of $\overline{FH}$, then $FG = GH$. So, $11x−7=3x + 9$.

Step2: Solve for x

Subtract $3x$ from both sides: $11x-3x - 7=3x-3x + 9$, which simplifies to $8x-7 = 9$. Then add 7 to both sides: $8x-7 + 7=9 + 7$, giving $8x=16$. Divide both sides by 8: $x=\frac{16}{8}=2$.

Step3: Find FG

Substitute $x = 2$ into the expression for $FG$. $FG=11x−7$, so $FG=11\times2−7=22 - 7=15$.

Answer:

15