We know that
• H is the midpoint of GI.
Since H is midpoint of GI, that means it divides the segment into two equal parts. In other words, GH is equal to HI.
[tex]\begin{gathered} GH=HI \\ 5x+2=9x-10 \end{gathered}[/tex]Now, we solve for x
[tex]\begin{gathered} 2+10=9x-5x \\ 4x=12 \\ x=\frac{12}{4}=3 \end{gathered}[/tex]We use this value to find GH
[tex]GH=5x+2=5(3)+2=15+2=17[/tex]