To find the length of [tex]\( GH \)[/tex] given the measurements [tex]\( FG = 2 \)[/tex] units, [tex]\( FI = 7 \)[/tex] units, and [tex]\( HI = 1 \)[/tex] unit, follow these steps:
1. Understand the relationship: We are given three lengths [tex]\( FG \)[/tex], [tex]\( FI \)[/tex], and [tex]\( HI \)[/tex]. The goal is to find the length of [tex]\( GH \)[/tex].
2. Identify the points and segments: We assume [tex]\( G \)[/tex], [tex]\( H \)[/tex], and [tex]\( I \)[/tex] are collinear points with [tex]\( G \)[/tex] and [tex]\( I \)[/tex] being at the extremities and [tex]\( H \)[/tex] lying somewhere in between.
3. Consider the total distance [tex]\( FI \)[/tex]. We want to express [tex]\( FI \)[/tex] as the sum of the segments [tex]\( FG \)[/tex], [tex]\( GH \)[/tex], and [tex]\( HI \)[/tex]:
[tex]\[
FI = FG + GH + HI
\][/tex]
4. Substitute the known values:
[tex]\[
7 = 2 + GH + 1
\][/tex]
5. Simplify the equation to isolate [tex]\( GH \)[/tex]:
[tex]\[
7 = 3 + GH
\][/tex]
6. Solve for [tex]\( GH \)[/tex]:
[tex]\[
GH = 7 - 3 = 4
\][/tex]
Therefore, the length of [tex]\( GH \)[/tex] is 4 units. The correct answer is:
[tex]\[ \boxed{4 \text{ units}} \][/tex]
