Find the distance between the points 

(

1

,

2

)

 and 

(

6

,

0

)

.

To find the distance between the points \((1, 2)\) and \((6, 0)\), we use the distance formula:

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

Given the points:

- \(x_1 = 1\), \(y_1 = 2\)
- \(x_2 = 6\), \(y_2 = 0\)

Substitute these values into the formula:

\[
\text{Distance} = \sqrt{(6 - 1)^2 + (0 - 2)^2}
\]

Simplify inside the square root:

\[
\text{Distance} = \sqrt{(5)^2 + (-2)^2} = \sqrt{25 + 4} = \sqrt{29}
\]

So, the distance between the points \((1, 2)\) and \((6, 0)\) is \(\sqrt{29}\), which is approximately 5.39 units.

Would you like more details or have any questions?

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Here are some related questions:

1. How would you calculate the distance between two points in a coordinate plane using the Pythagorean theorem?
2. What is the significance of the distance formula in geometry?
3. How do you find the midpoint of a line segment connecting two points?
4. What is the distance between the origin and a point \((x, y)\) in the coordinate plane?
5. How can the distance formula be applied in real-world scenarios?

**Tip:** Familiarize yourself with perfect squares to simplify square roots more quickly!

Learn how to calculate the distance between two points (1, 2) and (6, 0) in a coordinate plane using the distance formula. Understand the application of the Pythagorean theorem in finding distances between points. Suitable for students in Grades 6-8.

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