what is the distance between (−3,4) and (−8,−8)?

To find the distance between the points \((-3, 4)\) and \((-8, -8)\), we can use the distance formula:

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

Substituting the given points into the formula:

\[
\text{Distance} = \sqrt{((-8) - (-3))^2 + ((-8) - 4)^2}
\]

Simplify the expression inside the square root:

\[
\text{Distance} = \sqrt{(-8 + 3)^2 + (-8 - 4)^2} = \sqrt{(-5)^2 + (-12)^2}
\]

Calculate the squares:

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

Finally, take the square root:

\[
\text{Distance} = 13
\]

So, the distance between the points \((-3, 4)\) and \((-8, -8)\) is 13 units.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you derive the distance formula?
2. What is the midpoint between the points \((-3, 4)\) and \((-8, -8)\)?
3. How would the distance change if the points were \((3, 4)\) and \((8, 8)\)?
4. How do you find the slope of the line passing through \((-3, 4)\) and \((-8, -8)\)?
5. What are the coordinates of a point that is 5 units away from \((-3, 4)\) along the line to \((-8, -8)\)?

**Tip:** Remember, the distance formula is derived from the Pythagorean theorem applied to the difference in coordinates.

Learn how to calculate the distance between two points (-3, 4) and (-8, -8) using the distance formula and the Pythagorean theorem. This problem involves applying coordinate geometry concepts, including the distance formula and the Pythagorean theorem. Suitable for students in Grades 7-9.

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