To find the length of the diagonal of the rectangle formed by the points \( (-6, 8) \), \( (4, 8) \), \( (4, -3) \), and \( (-6, -3) \), we can use the distance formula.
First, we need to determine the coordinates of two opposite corners of the rectangle. We can select the points \( (-6, 8) \) and \( (4, -3) \).
The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting the coordinates \( (-6, 8) \) and \( (4, -3) \):
- \( x_1 = -6 \), \( y_1 = 8 \)
- \( x_2 = 4 \), \( y_2 = -3 \)
Now plug these values into the formula:
\[ d = \sqrt{(4 - (-6))^2 + (-3 - 8)^2} \] \[ d = \sqrt{(4 + 6)^2 + (-3 - 8)^2} \] \[ d = \sqrt{(10)^2 + (-11)^2} \] \[ d = \sqrt{100 + 121} \] \[ d = \sqrt{221} \]
Next, we compute the value of \( \sqrt{221} \):
\[ \sqrt{221} \approx 14.866 \]
Rounding this to the nearest hundredth, we find:
\[ \sqrt{221} \approx 14.87 \]
Thus, the length of the diagonal of the rectangle is approximately \( \boxed{14.87} \).