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The question involves finding the coordinates of point \( H \), which is the midpoint of segment \( FG \), given the following information:

- \( F \) is the midpoint of segment \( EG \).
- \( H \) is the midpoint of segment \( FG \).
- \( E \) is located at \( (-4, 1) \), and \( G \) is located at \( (6, -3) \).

Let's solve this step by step.

### Step 1: Find the coordinates of \( F \)
Since \( F \) is the midpoint of \( E \) and \( G \), we use the midpoint formula:

\[
\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

Substitute \( E(-4, 1) \) and \( G(6, -3) \):

\[
F = \left( \frac{-4 + 6}{2}, \frac{1 + (-3)}{2} \right) = \left( \frac{2}{2}, \frac{-2}{2} \right) = (1, -1)
\]

### Step 2: Find the coordinates of \( H \)
Now, \( H \) is the midpoint of \( F(1, -1) \) and \( G(6, -3) \). Using the midpoint formula again:

\[
H = \left( \frac{1 + 6}{2}, \frac{-1 + (-3)}{2} \right) = \left( \frac{7}{2}, \frac{-4}{2} \right) = \left( 3.5, -2 \right)
\]

Thus, the coordinates of \( H \) are \( (3.5, -2) \).

The correct answer is:
\[
\boxed{(3.5, -2)}
\]

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Would you like further details or clarification on any steps?

Here are 5 related questions to further explore this concept:
1. How would you find the midpoint if \( E \) and \( G \) were in 3D space?
2. Can you prove that a line segment's midpoint divides it into two equal parts using distance formulas?
3. What is the relationship between the slopes of \( EG \), \( FG \), and \( HG \)?
4. How would you find the length of segment \( EG \) using the distance formula?
5. How does the midpoint formula change when applied to a curved line (e.g., in polar coordinates)?

**Tip**: Midpoints are a foundational concept in coordinate geometry and can be extended to three dimensions or even used to find centroids of geometric shapes.

Four stores are located along a straight segment of Main Street, labeled E, F, G, and H. F is the midpoint of segment EG, and H is the midpoint of segment FG. A coordinate grid is superimposed, with E located at (-4, 1) and G located at (6, -3). What are the coordinates of H?

Learn how to determine the coordinates of point H, the midpoint of FG, with E and G located at (-4, 1) and (6, -3) respectively. This problem covers the midpoint formula and is suitable for students in Grades 8-10.

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