To find the length of segment [tex]\( GH \)[/tex] given the other segments, we start with the given information:
[tex]\[ FG = 2 \text{ units} \][/tex]
[tex]\[ FI = 7 \text{ units} \][/tex]
[tex]\[ HI = 1 \text{ unit} \][/tex]
We are to determine the length of segment [tex]\( GH \)[/tex]. The relationship provided in the problem can be described by the equation involving the segments:
[tex]\[ FI = FG + GH + HI \][/tex]
Substitute the given values into the equation:
[tex]\[ 7 = 2 + GH + 1 \][/tex]
Next, combine the known lengths on the right-hand side:
[tex]\[ 7 = 3 + GH \][/tex]
To isolate [tex]\( GH \)[/tex], subtract 3 from both sides of the equation:
[tex]\[ GH = 7 - 3 \][/tex]
Perform the subtraction:
[tex]\[ GH = 4 \][/tex]
Thus, the length of segment [tex]\( GH \)[/tex] is [tex]\( 4 \)[/tex] units. The correct answer is:
[tex]\[ \boxed{4 \text{ units}} \][/tex]
