https://file.aiquickdraw.com/mathbot/file/1729215892270y0p2jluz.jpg

To solve this problem, we will use the distance formula, which is:

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

The two points given are \( (2, 5) \) and \( (-6, -3) \). We will substitute these coordinates into the formula.

### Step 1: Label the coordinates
\[
(x_1, y_1) = (2, 5) \quad \text{and} \quad (x_2, y_2) = (-6, -3)
\]

### Step 2: Plug the values into the distance formula
\[
d = \sqrt{{(-6 - 2)^2 + (-3 - 5)^2}} = \sqrt{{(-8)^2 + (-8)^2}} = \sqrt{{64 + 64}} = \sqrt{128}
\]

### Step 3: Simplify the square root
\[
d = \sqrt{128} \approx 11.3
\]

So, the distance between the two points is approximately **11.3**, rounded to the nearest tenth.

Would you like more details on any step?

Here are 5 related questions to extend your understanding:

1. What is the distance between the points \( (1, 2) \) and \( (4, 6) \)?
2. How does the Pythagorean theorem relate to the distance formula?
3. What is the distance between \( (-3, -2) \) and \( (3, 4) \)?
4. Can the distance between two points ever be negative? Why or why not?
5. How would the formula change in 3D space?

**Tip:** Always double-check your signs when calculating the difference between coordinates to avoid errors.

Find the distance between the two points rounding to the nearest tenth: (2, 5) and (-6, -3).

This problem demonstrates how to find the distance between two points, (2, 5) and (-6, -3), using the distance formula √((x2 - x1)² + (y2 - y1)²). The solution simplifies to an approximate distance of 11.3. Perfect for students in Grades 8-10.

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