To find the length of the diagonal of the rectangle defined by the given points, we first need to determine the coordinates of the opposite corners of the rectangle. The points you provided are:
- \((-6, 8)\)
- \((4, 8)\)
- \((4, -3)\)
- \((-6, -3)\)
From these points, the rectangle can be visualized, and one diagonal can be formed using the points \((-6, 8)\) and \((4, -3)\).
To calculate the length of the diagonal, we can use the distance formula, which is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting the coordinates of the points \((-6, 8)\) and \((4, -3)\):
- \(x_1 = -6\)
- \(y_1 = 8\)
- \(x_2 = 4\)
- \(y_2 = -3\)
Substituting these values into the formula:
\[ d = \sqrt{(4 - (-6))^2 + (-3 - 8)^2} \] \[ = \sqrt{(4 + 6)^2 + (-3 - 8)^2} \] \[ = \sqrt{(10)^2 + (-11)^2} \] \[ = \sqrt{100 + 121} \] \[ = \sqrt{221} \]
Now, we can calculate \(\sqrt{221}\):
\[ \sqrt{221} \approx 14.835 \]
Rounding to the nearest hundredth, the length of the diagonal is approximately:
\[ \boxed{14.84} \text{ units} \]