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The problem asks us to find the coordinates of points \( B \) and \( E \), where:

- \( B \) is the midpoint of \( AC \),
- \( E \) is the midpoint of \( BD \).

We are given the coordinates of the points:
- \( A(-9, -4) \),
- \( C(-1, 6) \),
- \( D(-3, -7) \).

### Step 1: Finding \( B \) (midpoint of \( AC \))

The formula for the midpoint between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

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

For \( B \) (midpoint of \( AC \)):

\[
B = \left( \frac{-9 + (-1)}{2}, \frac{-4 + 6}{2} \right)
= \left( \frac{-10}{2}, \frac{2}{2} \right)
= (-5, 1)
\]

### Step 2: Finding \( E \) (midpoint of \( BD \))

Now, we use the midpoint formula again for \( B(-5, 1) \) and \( D(-3, -7) \):

\[
E = \left( \frac{-5 + (-3)}{2}, \frac{1 + (-7)}{2} \right)
= \left( \frac{-8}{2}, \frac{-6}{2} \right)
= (-4, -3)
\]

### Final Answer:

- The coordinates of \( B \) are \( (-5, 1) \),
- The coordinates of \( E \) are \( (-4, -3) \).

Let me know if you'd like further details or have any other questions!

Here are five related questions:
1. How do you find the midpoint of two points in 3D space?
2. What are the properties of a line segment's midpoint in geometry?
3

B is the midpoint of AC and E is the midpoint of BD. If A(-9,-4), C(-1,6), and D(-3,-7), find the coordinates of B and E.

Learn how to find the midpoints of line segments using the midpoint formula in coordinate geometry. In this problem, we calculate the coordinates of points B and E, given points A(-9,-4), C(-1,6), and D(-3,-7). Suitable for students in Grades 8-10.

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