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 for the diagonal between any two opposite corners.
We can use the points \((-6, 8)\) and \((4, -3)\) as the endpoints of the diagonal.
The distance formula is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
For our points:
- \(x_1 = -6\), \(y_1 = 8\)
- \(x_2 = 4\), \(y_2 = -3\)
Substituting the coordinates into the formula:
\[ d = \sqrt{(4 - (-6))^2 + (-3 - 8)^2} \]
Calculating the differences:
\[ 4 - (-6) = 4 + 6 = 10 \] \[ -3 - 8 = -11 \]
Now substituting these values back into the equation:
\[ d = \sqrt{(10)^2 + (-11)^2} \]
Calculating the squares:
\[ d = \sqrt{100 + 121} \]
\[ d = \sqrt{221} \]
Now, we calculate \(\sqrt{221}\):
\[ \sqrt{221} \approx 14.8661 \]
Rounding to the nearest hundredth, we get:
\[ d \approx 14.87 \]
Thus, the length of the diagonal of the rectangle is approximately 14.87.