What is the distance between line segment LN with endpoints L(1, 3) and N(7, 9)?

Solution:
1. Identify the coordinates of points L and N.
* Point L: (x_1, y_1) = (1, 3)
* Point N: (x_2, y_2) = (7, 9)

2. Use the distance formula between two points (x_1, y_1) and (x_2, y_2):
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

3. Substitute the given coordinates into the distance formula:
d = \sqrt{(7 - 1)^2 + (9 - 3)^2}

4. Simplify the expression:
d = \sqrt{6^2 + 6^2}
d = \sqrt{36 + 36}
d = \sqrt{72}

5. Simplify further if possible:
d = \sqrt{36 \cdot 2} = \sqrt{36} \cdot \sqrt{2} = 6\sqrt{2}

Result:
- The distance between L and N is 6\sqrt{2}.