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To find the distance between the points \((0, -2)\) and \((-4, -10)\), we use the distance formula:

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

Here, the coordinates of the two points are:
- \( (x_1, y_1) = (0, -2) \)
- \( (x_2, y_2) = (-4, -10) \)

Now, applying the formula:

\[
d = \sqrt{((-4) - 0)^2 + ((-10) - (-2))^2}
\]

Let's calculate that step by step:

1. \( (-4) - 0 = -4 \)
2. \( (-10) - (-2) = -10 + 2 = -8 \)

So, the formula becomes:

\[
d = \sqrt{(-4)^2 + (-8)^2} = \sqrt{16 + 64} = \sqrt{80}
\]

Now, simplify \( \sqrt{80} \):

\[
\sqrt{80} = \sqrt{16 \times 5} = 4\sqrt{5}
\]

Thus, the distance between the two points is:

\[
d = 4\sqrt{5} \text{ units}
\]

Would you like more details or further clarification on any step?

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Here are 5 related questions for practice:
1. Find the distance between the points \((1, 3)\) and \((4, -1)\).
2. Calculate the distance between \((-5, -7)\) and \((3, 2)\).
3. Determine the length of the diagonal of a rectangle with vertices at \((0, 0)\) and \((5, 12)\).
4. How do you calculate the distance between two points in three-dimensional space?
5. What is the relationship between the distance formula and the Pythagorean theorem?

**Tip**: Always simplify the radical in distance calculations whenever possible for the most accurate expression.

Find the distance between the points (0, -2) and (-4, -10).

Learn how to calculate the distance between the points (0, -2) and (-4, -10) using the distance formula. This problem involves key concepts in coordinate geometry and the Pythagorean Theorem. Perfect for students in Grades 8-10.

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