To find the length of [tex]\(GH\)[/tex], we need to understand the relationship between the given segments [tex]\(FG\)[/tex], [tex]\(FI\)[/tex], and [tex]\(HI\)[/tex]. Let's analyze the given information step-by-step.
We are given:
- [tex]\( FG = 2 \)[/tex] units
- [tex]\( FI = 7 \)[/tex] units
- [tex]\( HI = 1 \)[/tex] unit
We need to find the length of [tex]\( GH \)[/tex].
First, let's identify segment [tex]\(GH\)[/tex] within the context of segment [tex]\(FI\)[/tex].
- [tex]\(FI\)[/tex] is the entire length from point [tex]\(F\)[/tex] to point [tex]\(I\)[/tex].
- Segment [tex]\(FI\)[/tex] is divided into two parts: [tex]\(FG\)[/tex] and [tex]\(GH + HI\)[/tex].
From the given lengths:
- [tex]\( FG \)[/tex] is part of the segment from [tex]\(F\)[/tex] to [tex]\(G\)[/tex].
- [tex]\( HI \)[/tex] is part of the segment from [tex]\(H\)[/tex] to [tex]\(I\)[/tex].
We need to determine [tex]\(GH\)[/tex]. We can use the total length [tex]\(FI\)[/tex] to help us find the length of [tex]\(GH\)[/tex].
To calculate [tex]\(GH\)[/tex], we can denote:
[tex]\[ FI = FG + GH + HI \][/tex]
We rearrange this to express [tex]\(GH\)[/tex]:
[tex]\[ GH = FI - (FG + HI) \][/tex]
Substitute the known values into the equation:
[tex]\[ GH = 7 - (2 + 1) \][/tex]
[tex]\[ GH = 7 - 3 \][/tex]
[tex]\[ GH = 4 \][/tex]
Therefore, the length of [tex]\(GH\)[/tex] is 4 units.
The correct answer is: 4 units
