find the distance bettwen (-2,6) and (-8,-3) as a point

To find the distance between two points \((-2, 6)\) and \((-8, -3)\), we use the distance formula:

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

Here:
- \((x_1, y_1) = (-2, 6)\)
- \((x_2, y_2) = (-8, -3)\)

Substitute the values into the formula:

\[
d = \sqrt{(-8 - (-2))^2 + (-3 - 6)^2}
\]

Simplify the expression:

\[
d = \sqrt{(-8 + 2)^2 + (-3 - 6)^2}
= \sqrt{(-6)^2 + (-9)^2}
= \sqrt{36 + 81}
= \sqrt{117}
\]

So, the distance is:

\[
d = \sqrt{117} \approx 10.82
\]

The distance between the two points is approximately **10.82 units**.

Would you like more details or clarifications?

Here are 5 related questions for further exploration:
1. How would the distance formula change in 3D space?
2. What is the midpoint between the points \((-2, 6)\) and \((-8, -3)\)?
3. Can you find the equation of the line passing through these points?
4. How do you apply the distance formula in real-world problems?
5. What is the distance between \((-8, -3)\) and the origin \((0, 0)\)?

**Tip:** The distance formula is derived from the Pythagorean theorem applied to the differences in the coordinates of two points.

find the distance between (-2,6) and (-8,-3) as a point

Learn how to calculate the distance between the points (-2, 6) and (-8, -3) using the distance formula. This detailed step-by-step guide covers essential geometric concepts, including coordinate plane calculations and the Pythagorean theorem, suitable for students in Grades 8-10.

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