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The problem asks to find the coordinates of point \( B \), given the midpoint \( M(0, 1) \) of line segment \( AB \) and the coordinates of point \( A(-8, 8) \).

We use the midpoint formula:
\[
M(x, y) = \left( \frac{x_A + x_B}{2}, \frac{y_A + y_B}{2} \right)
\]
where \( (x_A, y_A) \) are the coordinates of point \( A \), and \( (x_B, y_B) \) are the coordinates of point \( B \).

Given:
- \( M(0, 1) \)
- \( A(-8, 8) \)

Using the midpoint formula:
\[
0 = \frac{-8 + x_B}{2} \quad \text{(for the x-coordinate)}
\]
\[
1 = \frac{8 + y_B}{2} \quad \text{(for the y-coordinate)}
\]

### Solve for \( x_B \):
\[
0 = \frac{-8 + x_B}{2}
\]
Multiply both sides by 2:
\[
0 = -8 + x_B
\]
Add 8 to both sides:
\[
x_B = 8
\]

### Solve for \( y_B \):
\[
1 = \frac{8 + y_B}{2}
\]
Multiply both sides by 2:
\[
2 = 8 + y_B
\]
Subtract 8 from both sides:
\[
y_B = -6
\]

Thus, the coordinates of point \( B \) are \( (8, -6) \).

Would you like more details or have any questions about this solution?

Here are 5 related questions for further practice:
1. If the midpoint is \( M(3, 4) \) and point \( A \) is \( (1, 2) \), what are the coordinates of point \( B \)?
2. How do you calculate the distance between two points in a plane?
3. Can you derive the equation of a line given two points?
4. What is the relationship between the slope of a line and its perpendicular bisector?
5. How does the midpoint formula relate to the distance formula?

**Tip**: The midpoint formula is simply the average of the x-coordinates and y-coordinates of two points.

The midpoint of AB is M(0, 1). If the coordinates of A are (-8, 8), what are the coordinates of B?

Learn how to find the coordinates of point B when the midpoint and one endpoint are given. This problem involves using the midpoint formula to solve for unknown coordinates. Suitable for students in Grades 8-10.

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