Find the distance between the points (

–

10,

–

10) and (

–

8,

–

8).

Write your answer as a whole number or a fully simplified radical expression. Do not round.

To find the distance between the two points \((-10, -10)\) and \((-8, -8)\), we can use the distance formula. The distance formula for two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Substituting the given points \((-10, -10)\) and \((-8, -8)\) into the formula, we identify:

- \(x_1 = -10\), \(y_1 = -10\)
- \(x_2 = -8\), \(y_2 = -8\)

Now plug these values into the formula:

\[
d = \sqrt{(-8 - (-10))^2 + (-8 - (-10))^2}
\]

\[
d = \sqrt{(-8 + 10)^2 + (-8 + 10)^2}
\]

\[
d = \sqrt{2^2 + 2^2}
\]

\[
d = \sqrt{4 + 4}
\]

\[
d = \sqrt{8}
\]

\[
d = \sqrt{4 \times 2}
\]

\[
d = 2\sqrt{2}
\]

So, the distance between the points \((-10, -10)\) and \((-8, -8)\) is \(2\sqrt{2}\).

Would you like more details or have any questions?

### Related Questions:
1. How would you find the distance between points in a three-dimensional space?
2. What is the distance between the points \((-3, -4)\) and \((1, 0)\)?
3. If the distance between two points is \(2\sqrt{2}\), what does this tell us about their relative positions?
4. How can the distance formula be derived from the Pythagorean theorem?
5. What happens to the distance formula if both points are on the same vertical or horizontal line?

### Tip:
Visualizing the points on a coordinate plane can help confirm the correctness of your calculation.

Learn how to calculate the distance between two points (-10, -10) and (-8, -8) using the distance formula. This problem involves applying the distance formula in coordinate geometry. Suitable for Grades 7-9.

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