The midpoint of start overline, AB, end overlineAB is M, left parenthesis, 0, comma, minus, 3, right parenthesis*M*(0,−3). If the coordinates of A*A* are left parenthesis, minus, 8, comma, minus, 2, right parenthesis(−8,−2), what are the coordinates of B*B*?

To find the coordinates of point \( B \), we again use the midpoint formula. The midpoint \( M(x, y) \) of a line segment between two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by:

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

In this problem:

- Midpoint \( M = (0, -3) \)
- Point \( A = (-8, -2) \)
- Point \( B = (x_2, y_2) \)

We need to find the coordinates of \( B(x_2, y_2) \).

### Step-by-Step Solution:

1. **Calculate the x-coordinate of B:**

   \[
   0 = \frac{-8 + x_2}{2}
   \]

   Multiply both sides by 2:

   \[
   0 = -8 + x_2
   \]

   Add 8 to both sides:

   \[
   x_2 = 8
   \]

2. **Calculate the y-coordinate of B:**

   \[
   -3 = \frac{-2 + y_2}{2}
   \]

   Multiply both sides by 2:

   \[
   -6 = -2 + y_2
   \]

   Add 2 to both sides:

   \[
   y_2 = -4
   \]

### Conclusion:

The coordinates of point \( B \) are \( (8, -4) \).

Would you like more details, or do you have any questions?

Here are 5 related questions for further exploration:
1. What is the formula for finding the midpoint of a line segment?
2. How can you determine the distance between two points using their coordinates?
3. How do you find the coordinates of a point if you know the midpoint and the other endpoint?
4. How is the midpoint formula derived?
5. What are some practical applications of finding midpoints in real-world scenarios?

**Tip:** Midpoint calculations are useful for dividing a line segment into two equal parts, which is particularly helpful in geometry and coordinate geometry.

Learn how to find the coordinates of point B using the midpoint formula and the coordinates of point A. This problem involves coordinate geometry and is suitable for students in Grades 7-9.

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