Find the distance between the points 

(

3

,

6

)

 and 

(

0

,

2

)

.

*Write* *your answer as a whole number or a fully simplified radical expression. Do not* *round.*

 units

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

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

Given the points \((3, 6)\) and \((0, 2)\), substitute the values into the formula:

\[
d = \sqrt{(0 - 3)^2 + (2 - 6)^2}
\]

Simplify the expressions inside the square root:

\[
d = \sqrt{(-3)^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25}
\]

Finally, take the square root:

\[
d = 5
\]

So, the distance between the points \((3, 6)\) and \((0, 2)\) is \( \mathbf{5} \) units.

Would you like more details or have any questions?

Here are some related questions you might find helpful:
1. How would the distance change if one of the points were negative?
2. Can you generalize the distance formula for 3-dimensional space?
3. How do you find the midpoint between the two points?
4. What is the slope of the line passing through these two points?
5. How does the Pythagorean theorem relate to the distance formula?

**Tip:** The distance formula is derived from the Pythagorean theorem, making it useful in problems involving right triangles.

Learn how to find the distance between two points (3, 6) and (0, 2) using the distance formula. This problem involves basic coordinate geometry concepts and applies the Pythagorean theorem. Suitable for students in Grades 6-8.

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