Calculate the distance of the two points (-4,2) and (-4,-4)

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

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

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

Substitute the values into the formula:

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

Simplify:

\[
\text{Distance} = \sqrt{(0)^2 + (-6)^2} = \sqrt{0 + 36} = \sqrt{36} = 6
\]

So, the distance between the points \((-4, 2)\) and \((-4, -4)\) is **6 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 \((-4, 2)\) and \((0, -4)\)?
2. What is the midpoint between the points \((-4, 2)\) and \((-4, -4)\)?
3. Can you explain how the distance formula is derived from the Pythagorean theorem?
4. How would the distance formula be applied in 3D space?
5. What happens to the distance between two points if both are shifted by the same amount in one direction?

**Tip:** When the x-coordinates of two points are the same, the distance between them is just the absolute difference between their y-coordinates.

Learn how to calculate the distance between two points (-4, 2) and (-4, -4) using the distance formula. This problem involves coordinate geometry and applies the Pythagorean theorem. Suitable for students in Grades 7-9.

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