Find the distance between the points (
–
5,2) and (0,
–
10).

To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in the coordinate plane, we use the distance formula:

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

Given the points \((-5, 2)\) and \((0, -10)\), let's plug the coordinates into the formula:

- \(x_1 = -5\), \(y_1 = 2\)
- \(x_2 = 0\), \(y_2 = -10\)

Substitute into the formula:

\[
d = \sqrt{(0 - (-5))^2 + (-10 - 2)^2}
\]
\[
d = \sqrt{(5)^2 + (-12)^2}
\]
\[
d = \sqrt{25 + 144}
\]
\[
d = \sqrt{169}
\]
\[
d = 13
\]

So, the distance between the points \((-5, 2)\) and \((0, -10)\) is **13 units**.

Would you like more details or have any questions? 

Here are 5 related questions:
1. How do you derive the distance formula?
2. Can the distance formula be used for 3-dimensional points?
3. What happens if the points are the same—how do you calculate that distance?
4. How would the formula change if the coordinates were in polar form?
5. What are some real-world applications where this formula is used?

**Tip**: Always double-check your signs when substituting into the distance formula to avoid common errors!

Find the distance between the points (-5, 2) and (0, -10).

Learn how to calculate the distance between two points in the coordinate plane using the distance formula. This problem shows the calculation between the points (-5, 2) and (0, -10), resulting in a distance of 13 units. Suitable for students in Grades 8-10.

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