what is the distance between k and J K is (0,-2) and J is (2,2)

To find the distance between two points \( K(0, -2) \) and \( J(2, 2) \), we use the distance formula:

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

Here, \( (x_1, y_1) = (0, -2) \) and \( (x_2, y_2) = (2, 2) \). Plugging these values into the formula:

\[
d = \sqrt{(2 - 0)^2 + (2 - (-2))^2}
\]
\[
d = \sqrt{(2)^2 + (2 + 2)^2}
\]
\[
d = \sqrt{4 + 16}
\]
\[
d = \sqrt{20}
\]
\[
d = 2\sqrt{5}
\]

So, the distance between points \( K \) and \( J \) is \( 2\sqrt{5} \), approximately \( 4.47 \).

Would you like any further details or have questions?

Here are 5 related questions to explore:
1. What is the midpoint between \( K \) and \( J \)?
2. How would you apply the distance formula in 3D space?
3. What is the distance between two points along a vertical or horizontal line?
4. Can you derive the distance formula from the Pythagorean theorem?
5. How does the distance formula change for points on a coordinate plane with different units?

**Tip**: Always double-check signs when plugging coordinates into formulas to avoid simple errors!

Learn how to calculate the distance between two points K(0, -2) and J(2, 2) using the distance formula. This problem explores key geometry concepts such as the distance between points on a coordinate plane, applying the Pythagorean theorem, and understanding coordinates. Suitable for students in Grades 7-9.

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