Find the distance between the two points rounding to the nearest tenth (if necessary).
left parenthesis, 2, comma, 5, right parenthesis, and , left parenthesis, minus, 6, comma, minus, 3, right parenthesis
(2,5) and (−6,−3)

To find the distance between the two points \((2, 5)\) and \((-6, -3)\), you can use the distance formula:

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

Substituting the given points \((x_1, y_1) = (2, 5)\) and \((x_2, y_2) = (-6, -3)\):

\[
\text{Distance} = \sqrt{(-6 - 2)^2 + (-3 - 5)^2}
\]

Simplify the expressions:

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

\[
\text{Distance} = \sqrt{64 + 64}
\]

\[
\text{Distance} = \sqrt{128}
\]

Finally, find the square root of 128 and round to the nearest tenth:

\[
\text{Distance} \approx 11.3
\]

So, the distance between the two points is approximately **11.3** units.

Would you like more details or have any questions?

Here are some related questions:
1. How would the distance change if both points were shifted 3 units to the right?
2. What is the midpoint of the points \((2, 5)\) and \((-6, -3)\)?
3. How do you derive the distance formula from the Pythagorean theorem?
4. Can the distance formula be used in three-dimensional space?
5. What is the significance of the distance formula in coordinate geometry?

**Tip:** Always double-check the coordinates and arithmetic when using the distance formula to avoid common mistakes.

Learn how to calculate the distance between two points (2, 5) and (-6, -3) using the distance formula. This problem involves applying the distance formula in coordinate geometry to find the distance rounded to the nearest tenth.

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