https://file.aiquickdraw.com/mathbot/file/172687167137511ew60qi.jpg

Let's break down the tasks from the provided image and solve them step by step.

1. **D is the midpoint of \( \overline{BG} \)**:
   - On the number line, \( B \) corresponds to -7 and \( G \) corresponds to -2.
   - The midpoint formula for a number line is:
     \[
     \text{Midpoint} = \frac{\text{Endpoint 1} + \text{Endpoint 2}}{2}
     \]
     Applying the values for \( B \) and \( G \):
     \[
     \frac{-7 + (-2)}{2} = \frac{-9}{2} = -4.5
     \]
     \( D \) is located at -5, not -4.5, so **this statement is false**.

2. **E is the midpoint of \( \overline{AI} \)**:
   - \( A \) is at -8, and \( I \) is at 0.
   - Again, applying the midpoint formula:
     \[
     \frac{-8 + 0}{2} = \frac{-8}{2} = -4
     \]
     \( E \) is located at -4, so **this statement is true**.

Next, find the midpoints of the points in the coordinate plane:

3. **Find the midpoint of \( A(1, 2) \) and \( B(-3, 6) \)**:
   - The midpoint formula for two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
     \[
     M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
     \]
     Substituting \( A(1, 2) \) and \( B(-3, 6) \):
     \[
     M = \left( \frac{1 + (-3)}{2}, \frac{2 + 6}{2} \right) = \left( \frac{-2}{2}, \frac{8}{2} \right) = (-1, 4)
     \]
     The midpoint is \( (-1, 4) \).

4. **Find the midpoint of \( A(6, -5) \) and \( B(8, -2) \)**:
   - Applying the midpoint formula again:
     \[
     M = \left( \frac{6 + 8}{2}, \frac{-5 + (-2)}{2} \right) = \left( \frac{14}{2}, \frac{-7}{2} \right) = (7, -3.5)
     \]
     The midpoint is \( (7, -3.5) \).

Let me know if you'd like more details or clarifications! 

Here are 5 related questions:
1. How do you calculate the midpoint between two coordinates?
2. What is the general formula for the midpoint of a segment on a number line?
3. If point C is at (-3) and point H is at (4), what is the midpoint of \( \overline{CH} \)?
4. How do you find the midpoint between two 3D points?
5. What happens to the midpoint if you shift the entire line by a certain value?

**Tip**: Always remember to add the corresponding coordinates when finding the midpoint, and then divide by 2.

Use the number line to tell whether each statement is true or false. D is the midpoint of BC. E is the midpoint of AT. Find the coordinates of M, the midpoint of AB, for each pair of points: (1,2) and (-3,6), (6,-5) and (8,-2).

Solve problems on finding midpoints both on a number line and in the coordinate plane. This task includes evaluating statements about midpoints and finding the midpoint for pairs of coordinates.

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