Question

if fg = 2 units, fi = 7 units, and hi = 1 unit, what is gh?
3 units
4 units
5 units
6 units

Explanation:

Step1: Find GI length

We know that \( FI = 7 \) units and \( HI = 1 \) unit. Also, \( FI=FG + GH+ HI \), but first we can find \( GI \) as \( FI - FG \)? Wait, no, let's correct. Wait, \( FI = FG + GH + HI \)? Wait, no, the points are F---G-------H---I---J. So \( FI = FG + GH + HI \)? Wait, no, actually, \( FI = FG + GH + HI \)? Wait, no, let's see: \( FI \) is from F to I, which is F to G (2) + G to H (let's call it x) + H to I (1). So \( FI = FG + GH + HI \). So \( 7=2 + x+ 1 \). Wait, but maybe another way: first find \( GI \). Wait, \( FI = 7 \), \( FG = 2 \), so \( GI=FI - FG=7 - 2 = 5 \)? No, that's wrong. Wait, no, \( FI \) is F to I, so F to G is 2, G to H is x, H to I is 1. So total \( FI = 2 + x + 1=7 \). So \( x + 3 =7 \), so \( x=4 \)? Wait, no, wait, maybe \( GI = FI - FG \)? Wait, no, \( FI \) is F to I, \( FG \) is F to G, so \( GI = FI - FG = 7 - 2 = 5 \). Then, since \( HI = 1 \), then \( GH = GI - HI = 5 - 1 = 4 \). Yes, that's better. So Step1: Calculate \( GI \) as \( FI - FG \).
\( GI = FI - FG = 7 - 2 = 5 \) units.

Step2: Calculate \( GH \) as \( GI - HI \)

We know \( GI = 5 \) units and \( HI = 1 \) unit. So \( GH = GI - HI = 5 - 1 = 4 \) units.

Answer:

4 units