Question

1. if g is the midpoint of fh, find fg. f 11x - 7 g 3x + 9 h

Explanation:

Step1: Use mid - point property

Since G is the mid - point 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: $8x-7 + 7=9 + 7$, getting $8x=16$. 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