Final answer:
To find the length of GF, set the expressions for GJ and JF equal since J is the midpoint. Solve for 'x', then add GJ and JF to get GF which is 108 units.
Step-by-step explanation:
Since J is the midpoint of GF, the lengths of GJ and JF are equal. Therefore, we can set the given expressions for GJ and JF equal to each other and solve for 'x'.
GJ = 7x - 9, and JF = 2x + 36. To find GF, which is the entire length of the segment, we need to add GJ and JF together once we have found the value of 'x'.
Let's set the expressions equal to each other since J is the midpoint:
7x - 9 = 2x + 36
Solving for 'x', we subtract 2x from both sides and add 9 to both sides:
7x - 2x = 36 + 9
5x = 45
x = 9
Now that we have the value of 'x', we calculate GF by adding GJ and JF:
GF = GJ + JF = (7x - 9) + (2x + 36)
We substitute x = 9 into the equation:
GF = (7(9) - 9) + (2(9) + 36) = 63 - 9 + 18 + 36 = 54 + 54 = 108
Therefore, the length of GF is 108 units.