To find the length of line segment $GH$ between the points $G(0, 3)$ and $H(-8, 7)$, we can use the distance formula, which is given by:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

For the points $G(0, 3)$ and $H(-8, 7)$, substitute $x_1 = 0$, $y_1 = 3$, $x_2 = -8$, and $y_2 = 7$ into the formula:

$d = \sqrt{(-8 - 0)^2 + (7 - 3)^2}$

$d = \sqrt{(-8)^2 + (4)^2}$

$d = \sqrt{64 + 16}$

$d = \sqrt{80}$

$d = 4\sqrt{5}$

The length of $GH$ is $4\sqrt{5}$, or approximately 8.94 units.

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. How would you find the length of the other sides, $HI$ and $GI$?
2. What is the perimeter of triangle $GHI$?
3. How can you use these coordinates to find the area of triangle $GHI$?
4. What type of triangle is $GHI$, based on its side lengths?
5. How do the slopes of the sides relate to the angles in triangle $GHI$?

Tip: Always double-check your arithmetic when using the distance formula!