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Find the distance between the points (8,9) and (2,1).

To find the distance between the points \((8, 9)\) and \((2, 1)\), you can use the distance formula:

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

Here, \((x_1, y_1)\) are the coordinates of the first point, and \((x_2, y_2)\) are the coordinates of the second point.

Substitute the given coordinates:

\[
d = \sqrt{(2 - 8)^2 + (1 - 9)^2}
\]

Simplify the expression inside the square root:

\[
d = \sqrt{(-6)^2 + (-8)^2} = \sqrt{36 + 64} = \sqrt{100}
\]

Finally, calculate the square root:

\[
d = 10
\]

So, the distance between the points \((8, 9)\) and \((2, 1)\) is **10 units**.

Would you like more details on the steps or have any questions?

Here are 5 related questions you might find interesting:
1. How would the distance formula change if we were working in three dimensions?
2. Can you derive the distance formula from the Pythagorean theorem?
3. What is the midpoint of the line segment connecting the points \((8, 9)\) and \((2, 1)\)?
4. How can the distance formula be applied in physics to find the displacement between two points?
5. What is the significance of the distance formula in coordinate geometry?

**Tip:** When calculating distances, always ensure to square the differences before adding, as this eliminates any negative values.

Find the distance between the points (8,9) and (2,1).

Discover how to calculate the distance between the points (8,9) and (2,1) using the distance formula in coordinate geometry. This problem is perfect for students in Grades 6-8 and covers essential concepts like the Pythagorean theorem and distance calculations.

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