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!