Find the distance between the points (2,2) and (7,1).

To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a plane, you can use the distance formula:

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

Given the points \((2, 2)\) and \((7, 1)\):

- \(x_1 = 2\), \(y_1 = 2\)
- \(x_2 = 7\), \(y_2 = 1\)

Substitute these values into the formula:

\[
\text{Distance} = \sqrt{(7 - 2)^2 + (1 - 2)^2}
\]

Simplify inside the square root:

\[
\text{Distance} = \sqrt{(5)^2 + (-1)^2} = \sqrt{25 + 1} = \sqrt{26}
\]

So, the distance between the points \((2, 2)\) and \((7, 1)\) is \(\sqrt{26}\), which is approximately 5.10 units.

Would you like more details or have any questions?

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Here are some related questions:

1. How do you calculate the midpoint between two points?
2. What is the formula for the slope of a line between two points?
3. How do you find the distance between points in 3D space?
4. What is the relationship between distance and displacement in physics?
5. Can you derive the distance formula from the Pythagorean theorem?

**Tip:** Always double-check your calculations when working with square roots to avoid small mistakes!

Learn how to find the distance between two points (2, 2) and (7, 1) using the distance formula. This problem involves basic coordinate geometry and the application of the distance formula. Suitable for students in Grades 7-9.

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