To find the distance of diagonal LN between the points \( L(-2, 3) \) and \( N(2, -3) \), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
In this case, let:
- \( (x_1, y_1) = (-2, 3) \) (point L)
- \( (x_2, y_2) = (2, -3) \) (point N)
Now plugging the coordinates into the distance formula:
\[ d = \sqrt{(2 - (-2))^2 + (-3 - 3)^2} \]
Calculating the differences:
\[ x_2 - x_1 = 2 - (-2) = 2 + 2 = 4 \] \[ y_2 - y_1 = -3 - 3 = -3 - 3 = -6 \]
Now substituting back into the distance formula:
\[ d = \sqrt{(4)^2 + (-6)^2} \] \[ d = \sqrt{16 + 36} \] \[ d = \sqrt{52} \]
Next, we can simplify \( \sqrt{52} \):
\[ \sqrt{52} = \sqrt{4 \times 13} = 2\sqrt{13} \]
Calculating \( 2\sqrt{13} \) using a calculator:
\[ \sqrt{13} \approx 3.60555 \] \[ 2\sqrt{13} \approx 2 \times 3.60555 \approx 7.2111 \]
Now rounding to the nearest hundredth:
\[ d \approx 7.21 \]
Thus, the distance of diagonal LN is approximately 7.21.