Answer:
[tex]GH=2\sqrt{10}[/tex]
Step-by-step explanation:
Considering each is square is 1x1.
We have the points G(-2, -3) and H(0, 3).
Using the distance formula:
[tex]$d=\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$[/tex]
[tex]$d=\sqrt{(-2 - 0)^2 + (-3 - 3)^2}$[/tex]
[tex]$d=\sqrt{(-2 )^2 + (-6)^2}$[/tex]
[tex]$d=\sqrt{4 +36}$[/tex]
[tex]d=\sqrt{40}=2\sqrt{10}[/tex]
Also, using the Pythagorean theorem:
[tex]a^2+b^2=c^2[/tex]
[tex]2^2+6^2=c^2[/tex]
[tex]4+36=c^2[/tex]
[tex]c=GH=\sqrt{40}=2\sqrt{10}[/tex]
