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

left parenthesis, 3, comma, minus, 4, right parenthesis, and , left parenthesis, 9, comma, minus, 9, right parenthesis

(3,−4) and (9,−9)

To find the distance between the two points \((3, -4)\) and \((9, -9)\), you can use the distance formula:

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

Substitute the given points into the formula:

\[
x_1 = 3, \, y_1 = -4, \, x_2 = 9, \, y_2 = -9
\]

\[
d = \sqrt{(9 - 3)^2 + (-9 - (-4))^2}
\]

Simplify the expressions inside the square root:

\[
d = \sqrt{(6)^2 + (-5)^2}
\]

Calculate the squares:

\[
d = \sqrt{36 + 25}
\]

Add the results:

\[
d = \sqrt{61}
\]

Finally, find the square root of 61 and round to the nearest tenth:

\[
d \approx 7.8
\]

So, the distance between the two points is approximately **7.8** units.

Would you like more details or have any questions?

Here are some related questions:
1. How is the distance formula derived?
2. What is the significance of each term in the distance formula?
3. Can you find the distance between two points in 3D space?
4. How would the formula change if the points had the same x-coordinates?
5. How would the formula change if the points had the same y-coordinates?
6. What is the distance between the origin and the point (9, -9)?
7. How can you use the Pythagorean theorem to find the distance between two points?
8. What is the effect of rounding on the accuracy of the distance?

**Tip:** When using the distance formula, always double-check your arithmetic steps to avoid simple errors!

Learn how to find the distance between two points (3, -4) and (9, -9) using the distance formula. Step-by-step solution with detailed arithmetic steps and rounding to the nearest tenth. Suitable for high school students studying coordinate geometry.

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