 Calculate the distance between the points (0,8) and (-5,2) in the coordinate plane

Give an exact answer (not a decimal approximation).

To calculate the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in the coordinate plane, we use the **distance formula**:

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

Given the points \((0, 8)\) and \((-5, 2)\):

\[
d = \sqrt{(-5 - 0)^2 + (2 - 8)^2}
\]

Now, simplify:

\[
d = \sqrt{(-5)^2 + (-6)^2}
\]
\[
d = \sqrt{25 + 36}
\]
\[
d = \sqrt{61}
\]

So, the exact distance between the points is:

\[
\boxed{\sqrt{61}}
\]

Would you like further details or have any questions?

Here are 5 related questions for further practice:

1. What is the distance between the points \((3, 7)\) and \((8, 1)\)?
2. Find the midpoint between the points \((0, 8)\) and \((-5, 2)\).
3. How would the distance change if the points were reflected across the y-axis?
4. What is the distance between \((x_1, y_1)\) and \((x_2, y_2)\) in 3-dimensional space?
5. How does the distance formula relate to the Pythagorean Theorem?

**Tip:** Always simplify expressions inside the square root before finding the final result to avoid unnecessary steps.

Calculate the distance between the points (0,8) and (-5,2) in the coordinate plane. Give an exact answer (not a decimal approximation).

Learn how to calculate the exact distance between the points (0,8) and (-5,2) using the distance formula. This problem explores key concepts in coordinate geometry and applies the Pythagorean Theorem. Suitable for students in Grades 7-9.

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