Find the distance between the two points rounding to the nearest tenth (if necessary).
left parenthesis, minus, 4, comma, 5, right parenthesis, and , left parenthesis, minus, 9, comma, minus, 7, right parenthesis
(−4,5) and (−9,−7)

To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a coordinate plane, we use the distance formula:

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

Given the points \((-4, 5)\) and \((-9, -7)\), let's substitute the coordinates into the formula:

\[
\text{Distance} = \sqrt{(-9 - (-4))^2 + (-7 - 5)^2}
\]

Simplify the expressions inside the square root:

\[
\text{Distance} = \sqrt{(-9 + 4)^2 + (-7 - 5)^2}
\]
\[
\text{Distance} = \sqrt{(-5)^2 + (-12)^2}
\]
\[
\text{Distance} = \sqrt{25 + 144}
\]
\[
\text{Distance} = \sqrt{169}
\]
\[
\text{Distance} = 13
\]

So, the distance between the two points is \(13\).

Would you like more details or have any questions? Here are 5 related questions:

1. How would you apply the distance formula in three-dimensional space?
2. What is the midpoint of the two points \((-4, 5)\) and \((-9, -7)\)?
3. How does the distance formula relate to the Pythagorean theorem?
4. What are other methods to verify the distance between two points?
5. How can you use the distance formula in real-world applications?

**Tip:** Always check your calculations step by step, especially when dealing with negatives, to avoid errors.

Learn how to calculate the distance between two points (-4, 5) and (-9, -7) in a coordinate plane using the distance formula. This problem covers key concepts in coordinate geometry and involves applying the distance formula theorem. Suitable for students in Grades 9-12.

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