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

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

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

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

Substitute the values into the formula:

\[
d = \sqrt{(-3 - (-6))^2 + (9 - 8)^2}
\]
\[
d = \sqrt{(-3 + 6)^2 + (9 - 8)^2}
\]
\[
d = \sqrt{(3)^2 + (1)^2}
\]
\[
d = \sqrt{9 + 1} = \sqrt{10}
\]

So, the distance between the two points is:

\[
d = \sqrt{10} \approx 3.16
\]

Would you like more details on this? 

Here are some related questions:
1. How do you calculate distances in 3D space?
2. What is the midpoint between two points?
3. Can the distance formula be derived from the Pythagorean theorem?
4. What is the significance of the distance formula in coordinate geometry?
5. How can you determine the distance between a point and a line?

**Tip:** Always double-check your signs when using the distance formula to avoid errors in calculation.

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

Learn how to calculate the distance between two points (-6,8) and (-3,9) using the distance formula in coordinate geometry. This step-by-step solution demonstrates how to apply the formula and simplifies √10 to 3.16. Ideal for students in Grades 8-10.

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