To find the distance of the diagonal \( LN \), we can use the distance formula, which is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, the coordinates of points \( L \) and \( N \) are:
- \( L (-2, 3) \) where \( x_1 = -2 \) and \( y_1 = 3 \)
- \( N (2, -3) \) where \( x_2 = 2 \) and \( y_2 = -3 \)
Now, we can plug these values into the distance formula:
\[ d = \sqrt{(2 - (-2))^2 + (-3 - 3)^2} \]
This simplifies to:
\[ d = \sqrt{(2 + 2)^2 + (-3 - 3)^2} \] \[ d = \sqrt{(4)^2 + (-6)^2} \] \[ d = \sqrt{16 + 36} \] \[ d = \sqrt{52} \]
Calculating \( \sqrt{52} \):
\[ \sqrt{52} = \sqrt{4 \times 13} = 2\sqrt{13} \]
Now calculating \( 2\sqrt{13} \):
Using a calculator, we find:
\[ \sqrt{13} \approx 3.60555 \] Thus, \[ 2\sqrt{13} \approx 2 \times 3.60555 \approx 7.2111 \]
Rounding to the nearest hundredth:
\[ d \approx 7.21 \]
Therefore, the distance of diagonal \( LN \) rounded to the nearest hundredth is \( \boxed{7.21} \).