Question

g is the midpoint of $overline{fh}$. if $gh = x + 9$ and $fh = 11x + 9$, what is $fh?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since G is the midpoint of FH, then FH = 2GH. We know GH=x + 9 and FH=11x + 9. So, 11x+9 = 2(x + 9).

Step2: Expand the right - hand side

Expand 2(x + 9) to get 2x+18. The equation becomes 11x + 9=2x + 18.

Step3: Solve for x

Subtract 2x from both sides: 11x-2x + 9=2x-2x + 18, which simplifies to 9x+9 = 18. Then subtract 9 from both sides: 9x+9 - 9=18 - 9, giving 9x=9. Divide both sides by 9: x = 1.

Step4: Find FH

Substitute x = 1 into the expression for FH. FH=11x + 9, so FH=11(1)+9=11 + 9=20.

Answer:

20