What is the distance between points F(2, 9) and G(−2, 6)? Round to the nearest whole number.

To find the distance between two points, we use the **distance formula**:

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

Given points \( F(2, 9) \) and \( G(-2, 6) \), we can substitute the coordinates into the formula:

\[
d = \sqrt{((-2 - 2)^2 + (6 - 9)^2)}
\]

Simplifying the values:

\[
d = \sqrt{((-4)^2 + (-3)^2)} = \sqrt{(16 + 9)} = \sqrt{25} = 5
\]

Therefore, the distance between the points \( F(2, 9) \) and \( G(-2, 6) \) is **5 units**.

Would you like more details on any part of this explanation? Here are five related questions:

1. How is the distance formula derived from the Pythagorean theorem?
2. What is the distance between points \( (0, 0) \) and \( (5, 12) \)?
3. How can we extend this concept to three-dimensional space?
4. Can you find the midpoint between \( F(2, 9) \) and \( G(-2, 6) \)?
5. How would you solve for the distance if the points had variables instead of constants?

**Tip:** The distance formula is essentially the Pythagorean theorem applied to coordinate geometry!

Learn how to calculate the distance between points F(2, 9) and G(-2, 6) using the distance formula. This problem explores key concepts in coordinate geometry and the Pythagorean theorem, making it suitable for students in Grades 8-10.

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