What is the distance between (-6, 8)and
(-3, 9)

To find the distance between two points \((-6, 8)\) and \((-3, 9)\), we can use the distance formula:

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

Here:
- \((x_1, y_1) = (-6, 8)\)
- \((x_2, y_2) = (-3, 9)\)

Now, substitute the values:

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

Simplifying the expression:

\[
d = \sqrt{(3)^2 + (1)^2} = \sqrt{9 + 1} = \sqrt{10}
\]

Thus, the distance between the points is \(\sqrt{10}\), which is approximately \(3.16\) units.

Would you like more details or have any questions?

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Here are five related questions to expand on this:
1. What is the distance formula derived from?
2. How do you calculate the midpoint between two points?
3. Can the distance formula be extended to three dimensions?
4. What is the significance of the square root in the distance formula?
5. How do you find the slope between two points?

**Tip**: Always double-check your subtraction steps when using the distance formula to avoid mistakes.

What is the distance between (-6, 8) and (-3, 9)?

Discover how to calculate the distance between two points (-6, 8) and (-3, 9) using the distance formula. This problem explores key concepts in coordinate geometry, applying the Pythagorean theorem, with the solution resulting in √10 or approximately 3.16 units. Ideal for students in Grades 6-8.

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