The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in the coordinate plane is calculated using the distance formula:

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

For the points $C = (-5, -5)$ and $K = (1, 8)$, we can substitute into the formula:

$d = \sqrt{(1 - (-5))^2 + (8 - (-5))^2}$ $d = \sqrt{(1 + 5)^2 + (8 + 5)^2}$ $d = \sqrt{6^2 + 13^2}$ $d = \sqrt{36 + 169}$ $d = \sqrt{205}$ $d \approx 14.32$

Thus, the distance between points $C$ and $K$ is approximately $14.32$ units.

Would you like further details or have any questions?

Here are 5 related questions for further exploration:

1. How is the midpoint between points $C$ and $K$ calculated?
2. What is the slope of the line passing through points $C$ and $K$?
3. Can you find another pair of points that would be equidistant from both $C$ and $K$?
4. How would the distance formula change in three-dimensional space?
5. Can you find the equation of the line that passes through $C$ and $K$?

Tip: When dealing with distances in the coordinate plane, always ensure you've correctly squared the differences between the x- and y-coordinates.