Calculate the distance between the points C = (-5, -5) and K = (1, 8) in the coordinate plane.

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.

Learn how to calculate the distance between points C(-5,-5) and K(1,8) in the coordinate plane using the distance formula. This problem covers essential geometry concepts and applies the Pythagorean Theorem. Suitable for students in Grades 8-10.

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