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.