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

To find the distance between two points \((-6, 8)\) and \((-3, 9)\) in a coordinate plane, you can use the distance formula:

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

Here, \((x_1, y_1) = (-6, 8)\) and \((x_2, y_2) = (-3, 9)\). Plugging in the values:

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

Simplifying further:

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

So, the distance between the points is \(\sqrt{10}\).

Would you like more details or have any questions about this solution?

Here are 5 related questions you might find interesting:
1. How do you find the midpoint between two points in a coordinate plane?
2. What is the slope of the line passing through points \((-6, 8)\) and \((-3, 9)\)?
3. How do you find the equation of a line given two points?
4. What is the distance between the origin and the point \((4, 5)\)?
5. How do you use the Pythagorean Theorem to find the distance between two points?

**Tip:** When using the distance formula, remember that the order of subtraction doesn’t matter because the distance squared will eliminate any negative signs.

Learn how to calculate the distance between two points (-6, 8) and (-3, 9) using the distance formula in coordinate geometry. This problem involves finding the distance between specified points on a coordinate plane. Suitable for students in Grades 7-9.

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