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To solve this problem, we need to calculate the distance between two points \( K(1, -5) \) and \( H(8, 9) \) on the coordinate plane. We will use the distance formula:

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

Here:
- \( K(x_1, y_1) = (1, -5) \)
- \( H(x_2, y_2) = (8, 9) \)

Substitute these coordinates into the formula:

\[
d = \sqrt{(8 - 1)^2 + (9 - (-5))^2}
\]
\[
d = \sqrt{(7)^2 + (14)^2}
\]
\[
d = \sqrt{49 + 196}
\]
\[
d = \sqrt{245}
\]

Thus, the exact distance between points \( K \) and \( H \) is:

\[
d = \sqrt{245}
\]

Would you like a further explanation or details? 

Here are 5 related questions you might want to explore:
1. How do you find the midpoint between two points?
2. What is the slope of the line passing through these points?
3. How can you verify if two points are equidistant from a third point?
4. What is the geometric meaning of the distance formula?
5. Can the distance formula be extended to three-dimensional space?

**Tip**: Always square the differences first before adding them to avoid negative distance values!

Calculate the distance between the points K(1, -5) and H(8, 9) in the coordinate plane. Give an exact answer (not a decimal approximation).

Learn how to calculate the distance between two points K(1, -5) and H(8, 9) on a coordinate plane using the distance formula. This detailed step-by-step solution is suitable for students in Grades 8-10.

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