Find the distance between the points (8,-1) and (-4,-6)

To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) on a coordinate plane, you can use the distance formula:

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

Given the points \((8, -1)\) and \((-4, -6)\), we can plug in the values:

\[
\text{Distance} = \sqrt{((-4) - 8)^2 + ((-6) - (-1))^2}
\]

Now, calculate the differences:

\[
\text{Distance} = \sqrt{(-12)^2 + (-5)^2}
\]

Square the differences:

\[
\text{Distance} = \sqrt{144 + 25} = \sqrt{169}
\]

Finally, take the square root:

\[
\text{Distance} = 13
\]

So, the distance between the points \((8, -1)\) and \((-4, -6)\) is \(13\) units.

Would you like more details or have any questions?

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Here are 5 related questions:

1. How would you find the midpoint between the points \((8, -1)\) and \((-4, -6)\)?
2. What is the formula for finding the slope of the line passing through these two points?
3. How would you write the equation of the line that passes through these two points?
4. What is the distance between the origin and the point \((8, -1)\)?
5. How do you find the equation of the circle that has these two points as the diameter?

**Tip:** The distance formula is derived from the Pythagorean theorem and is a fundamental tool in coordinate geometry.

Learn how to calculate the distance between two points (8, -1) and (-4, -6) on a coordinate plane using the distance formula. This problem covers fundamental concepts in coordinate geometry, including the distance formula and Pythagorean theorem. Suitable for students in Grades 7-9.

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