Calculate the distance between the two points (-4,7) and (-2,5)

To calculate the distance between the two points \((-4, 7)\) and \((-2, 5)\), you can use the distance formula:

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

Given points:
\[
(x_1, y_1) = (-4, 7)
\]
\[
(x_2, y_2) = (-2, 5)
\]

Substitute the values into the formula:

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

Simplify the expressions:

\[
\text{Distance} = \sqrt{(2)^2 + (-2)^2}
\]
\[
\text{Distance} = \sqrt{4 + 4} = \sqrt{8}
\]

Simplify the square root:

\[
\text{Distance} = \sqrt{8} = 2\sqrt{2} \approx 2.83
\]

So, the distance between the points \((-4, 7)\) and \((-2, 5)\) is \(2\sqrt{2}\), which is approximately **2.83 units**.

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How would the distance change if the points were \((-4, 7)\) and \((-2, 9)\)?
2. What is the midpoint between the points \((-4, 7)\) and \((-2, 5)\)?
3. How do you calculate the distance between points on a 3D coordinate plane?
4. How does the Pythagorean theorem relate to the distance formula?
5. What is the length of the line segment connecting the points \((-4, 7)\) and \((-2, 5)\) in a coordinate plane?

**Tip:** Remember that the distance between two points in a coordinate plane is always a positive number, as it represents a physical length.

Learn how to calculate the distance between two points (-4, 7) and (-2, 5) using the distance formula. This problem covers coordinate geometry and the application of the distance formula in calculating lengths between points. Suitable for students in Grades 7-9.

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