To solve the problem of calculating the distance between the points $A = (0, 0)$ and $B = (-4, -8)$ in the coordinate plane, we use the distance formula:

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

Here:

• $(x_1, y_1) = (0, 0)$
• $(x_2, y_2) = (-4, -8)$

Substitute these values into the formula:

$d = \sqrt{(-4 - 0)^2 + (-8 - 0)^2}$ $d = \sqrt{(-4)^2 + (-8)^2}$ $d = \sqrt{16 + 64}$ $d = \sqrt{80}$ $d \approx 8.94$

Thus, the distance between the points $A$ and $B$ is approximately 8.94 units when rounded to the nearest hundredth.

Would you like further details or have any questions?

Here are some related questions for further practice:

1. How do you calculate the distance between two points with fractional coordinates?
2. What is the significance of the distance formula in geometry?
3. Can the distance formula be used in three-dimensional space? How?
4. How does the distance formula relate to the Pythagorean Theorem?
5. If the coordinates were decimals instead of integers, how would that affect the calculation?

Tip: Always double-check your arithmetic calculations, especially when squaring negative numbers, to avoid simple errors.