Find the distance between the given points. Round your answers to the nearest tenth if necessary. (-6, -2) (2, 7)

To find the distance between the points \((-6, -2)\) and \((2, 7)\), you can use the distance formula:

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

Substitute the given points \((-6, -2)\) and \((2, 7)\) into the formula:

\[
d = \sqrt{{(2 - (-6))}^2 + {(7 - (-2))}^2}
\]

Simplify the expression:

\[
d = \sqrt{{(2 + 6)}^2 + {(7 + 2)}^2}
\]
\[
d = \sqrt{{8}^2 + {9}^2}
\]
\[
d = \sqrt{64 + 81}
\]
\[
d = \sqrt{145}
\]

Now, take the square root of 145:

\[
d \approx 12.0
\]

So, the distance between the points \((-6, -2)\) and \((2, 7)\) is approximately **12.0** units.

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. How would you find the midpoint between these two points?
2. What is the slope of the line passing through these points?
3. Can you determine the equation of the line that passes through these points?
4. What is the distance between points \((1, 2)\) and \((4, 6)\)?
5. How does the distance formula relate to the Pythagorean theorem?

**Tip:** When working with the distance formula, always double-check your arithmetic operations to ensure accuracy.

Learn how to calculate the distance between two points (-6, -2) and (2, 7) using the distance formula. This problem involves applying coordinate geometry concepts and the distance formula theorem. Suitable for students in Grades 7-9.

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