Find the distance between the two points rounding *to the nearest tenth* (if necessary).

left parenthesis, minus, 5, comma, 4, right parenthesis, and , left parenthesis, 4, comma, minus, 8, right parenthesis

(−5,4) and (4,−8)

To find the distance between the two points \((-5, 4)\) and \((4, -8)\), use the distance formula:

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

Substitute the coordinates of the points into the formula:

\[
x_1 = -5, \, y_1 = 4, \, x_2 = 4, \, y_2 = -8
\]

\[
d = \sqrt{(4 - (-5))^2 + (-8 - 4)^2}
\]

Simplify the expressions inside the square root:

\[
d = \sqrt{(4 + 5)^2 + (-8 - 4)^2}
\]

\[
d = \sqrt{(9)^2 + (-12)^2}
\]

Calculate the squares:

\[
d = \sqrt{81 + 144}
\]

Add the results:

\[
d = \sqrt{225}
\]

Finally, find the square root of 225:

\[
d = 15
\]

So, the distance between the two points is **15** units.

Would you like more details or have any questions?

Here are some related questions:
1. What are the key steps in applying the distance formula?
2. How does changing the sign of coordinates affect the distance?
3. How can you check your work when using the distance formula?
4. What happens if both points are on the same line?
5. How can the distance formula be applied in real-world scenarios?
6. How do you find the midpoint between two points?
7. What is the distance between the origin and the point (4, -8)?
8. How would you calculate the distance if one coordinate was missing?

**Tip:** For easier calculations, consider simplifying the arithmetic inside the square root before proceeding to the final steps.

Learn how to find the distance between two points (-5, 4) and (4, -8) using the distance formula. This problem covers key concepts in coordinate geometry, including calculating distances using square roots. Suitable for high school students.

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