Final answer:
To find GH when g is the midpoint of FH, we divide the length of FH (11x - 9) by 2. The correct expression for GH would be (11x - 9)/2, which simplifies to 5.5x - 4.5. However, due to the given answer choices, it appears there may be a typo as none of the options are correct.
Step-by-step explanation:
If g is the midpoint of FH and FH = 11x - 9, we need to determine the length of GH. The property of a midpoint tells us that g divides FH into two equal parts. Therefore, the length of GH would be half the length of FH.
To find GH, we take the expression for the full length of FH, which is 11x - 9, and divide it by 2:
GH = (11x - 9) / 2
Now, we look at the possible answers to see which one could be equal to half of 11x - 9. By inspecting the answer choices, we can dismiss the options that do not match the form of the expression obtained by halving 11x - 9.
The correct answer is b) 5x - 3.5 because:
GH = (11x - 9) / 2
= (11/2)x - 9/2
= 5.5x - 4.5
However, since none of the choices match this expression exactly and all given choices are in the form of whole number coefficients, this seems like a typo in the answers. We would need to report this discrepancy as none of the options correctly represent GH = (11x - 9) / 2.