if points (-6,8) and (-1,-4) are plotted Find the distance between the two points in simplest radical form.

To find the distance between two points \((-6, 8)\) and \((-1, -4)\), we use the **distance formula**:

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

Here:
- \(x_1 = -6\), \(y_1 = 8\)
- \(x_2 = -1\), \(y_2 = -4\)

Now substitute the values into the formula:

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

Simplifying the terms inside the parentheses:

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

Now square the values:

\[
d = \sqrt{25 + 144} = \sqrt{169}
\]

The square root of 169 is 13, so the distance between the two points is:

\[
d = 13
\]

Would you like a more detailed explanation on any part of this? Here are some related questions you might consider:

1. How can the distance formula be derived from the Pythagorean theorem?
2. What is the distance between two points in three-dimensional space?
3. Can the distance formula be applied to points on a number line?
4. How does the distance formula change for non-Euclidean spaces?
5. How would you find the midpoint between the same two points?

**Tip:** The distance formula is essentially an application of the Pythagorean theorem in a coordinate plane.

If points (-6, 8) and (-1, -4) are plotted, find the distance between the two points in simplest radical form.

Learn how to find the distance between two points (-6, 8) and (-1, -4) using the distance formula. This problem covers key concepts in coordinate geometry and applies the Pythagorean theorem, making it suitable for students in Grades 8-10.

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