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To calculate the distance between the points \( G = (0, -8) \) and \( M = (5, -3) \) in the coordinate plane, we can use the distance formula:

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

Where:
- \( (x_1, y_1) = (0, -8) \) (coordinates of point \( G \)),
- \( (x_2, y_2) = (5, -3) \) (coordinates of point \( M \)).

Now, applying the coordinates into the formula:

\[
d = \sqrt{(5 - 0)^2 + (-3 + 8)^2}
\]
\[
d = \sqrt{(5)^2 + (5)^2}
\]
\[
d = \sqrt{25 + 25}
\]
\[
d = \sqrt{50}
\]
\[
d = 5\sqrt{2}
\]

So, the exact distance between points \( G \) and \( M \) is \( 5\sqrt{2} \).

Would you like a detailed breakdown of the steps or have any questions?

Here are 5 related questions you might find useful:
1. How does the distance formula relate to the Pythagorean theorem?
2. What is the significance of finding exact distances versus decimal approximations?
3. Can you apply the distance formula to 3D points?
4. How would the distance change if the points were reflected over the x-axis?
5. What are some applications of the distance formula in physics or geometry?

**Tip**: Always check if the result can be simplified when using square roots in distance calculations to avoid unnecessary complexity.

Calculate the distance between the points G = (0, -8) and M = (5, -3) in the coordinate plane. Give an exact answer (not a decimal approximation).

Learn how to calculate the exact distance between the points G(0, -8) and M(5, -3) in the coordinate plane using the distance formula. This solution is suitable for students in Grades 8-10 and involves applying the Pythagorean Theorem.

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