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To find the coordinates of point \( B \), we use the midpoint formula:

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

where \( A(x_1, y_1) \) and \( B(x_2, y_2) \) are the coordinates of points \( A \) and \( B \), and the midpoint is given as \( (0, 1) \).

From the problem:
- The coordinates of \( A \) are \( (-5, -2) \).
- The midpoint of \( \overline{AB} \) is \( (0, 1) \).

We can set up the following system of equations for \( B(x_2, y_2) \):

\[
\frac{-5 + x_2}{2} = 0 \quad \text{(for the x-coordinate)}
\]
\[
\frac{-2 + y_2}{2} = 1 \quad \text{(for the y-coordinate)}
\]

### Solving for \( x_2 \):
\[
\frac{-5 + x_2}{2} = 0
\]
Multiply both sides by 2:
\[
-5 + x_2 = 0
\]
Add 5 to both sides:
\[
x_2 = 5
\]

### Solving for \( y_2 \):
\[
\frac{-2 + y_2}{2} = 1
\]
Multiply both sides by 2:
\[
-2 + y_2 = 2
\]
Add 2 to both sides:
\[
y_2 = 4
\]

Thus, the coordinates of \( B \) are \( (5, 4) \).

Would you like more details or have any questions? Here are some additional related questions:

1. How do we calculate the midpoint if both coordinates are unknown?
2. Can you derive the formula for the midpoint from first principles?
3. What are some practical applications of the midpoint formula?
4. If the midpoint is changed to another point, how would the coordinates of \( B \) change?
5. How can we extend this to 3D geometry, if we had three coordinates for each point?

**Tip**: When using the midpoint formula, remember it essentially averages the x-coordinates and y-coordinates of the two points.

Find the coordinate of B if the midpoint of AB is at (0,1) and A is at (-5,-2).

Learn how to find the coordinate of point B given the midpoint (0, 1) and point A (-5, -2) using the midpoint formula. This problem involves coordinate geometry and is suitable for students in Grades 9-10.

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