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We are given the coordinates of the endpoints of \( \overline{FG} \) as \( F(-8, 3) \) and \( G(-2, -9) \), and point \( H \) divides the line segment such that the ratio \( FH:GH = 1:2 \). This suggests that \( H \) divides the segment in a 1:2 ratio.

To find the coordinates of \( H \), we use the section formula (or the formula for a point dividing a line segment in a given ratio):

\[
(x_H, y_H) = \left( \frac{m \cdot x_2 + n \cdot x_1}{m + n}, \frac{m \cdot y_2 + n \cdot y_1}{m + n} \right)
\]
where \( (x_1, y_1) \) are the coordinates of point \( F \), \( (x_2, y_2) \) are the coordinates of point \( G \), and \( m:n \) is the given ratio.

Here:
- \( F(-8, 3) \) and \( G(-2, -9) \)
- Ratio \( FH:GH = 1:2 \), so \( m = 1 \) and \( n = 2 \)

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Here are some related questions that might interest you:
1. What is the section formula and how does it work?
2. How do you calculate the ratio of a divided line segment?
3. Can you use the section formula in three dimensions?
4. What are some real-world applications of dividing a line segment in a ratio?
5. How do you find the midpoint of a line segment using coordinates?

**Tip:** The section formula is very useful in geometry when working with points dividing line segments into specific ratios!

The coordinates of the endpoints of FG are F(-8, 3) and G(-2, -9). Point H is on FG and divides it such that FH:GH is 1:2. What are the coordinates of H?

Learn how to find the coordinates of a point dividing a line segment using the section formula. In this problem, we calculate the coordinates of point H, which divides the line segment FG in the ratio 1:2. Suitable for students in Grades 9-12 studying coordinate geometry.

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