To find the length of line segment $AB$, we use the distance formula:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Where:

• $(x_1, y_1)$ is point $A (-5, -4)$
• $(x_2, y_2)$ is point $B (-3, 3)$

Substitute the coordinates into the formula:

$d = \sqrt{(-3 - (-5))^2 + (3 - (-4))^2}$ $d = \sqrt{(-3 + 5)^2 + (3 + 4)^2}$ $d = \sqrt{(2)^2 + (7)^2}$ $d = \sqrt{4 + 49} = \sqrt{53}$ $d \approx 7.28$

So, the length of $AB$ is approximately 7.28 units.

Would you like more details or have any questions?

Here are 5 related questions:

1. How do we find the midpoint of $AB$?
2. How would the distance change if the coordinates of $A$ and $B$ were swapped?
3. What is the equation of the line passing through $A$ and $B$?
4. How do we compute the slope of the line segment $AB$?
5. Can we calculate the distance between any two points in 3D space using a similar method?

Tip: The distance formula is derived from the Pythagorean Theorem. You are essentially calculating the hypotenuse of a right triangle formed by the horizontal and vertical distances between two points.