the midpoint of line AB is M(4-4). If the coordinates of A are (-3,1) what are the coordinates of B?

To find the coordinates of point \( B \), we 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 \( M = (4, -4) \)
- Point \( A = (-3, 1) \)
- 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:**

   \[
   4 = \frac{-3 + x_2}{2}
   \]

   Multiply both sides by 2:

   \[
   8 = -3 + x_2
   \]

   Add 3 to both sides:

   \[
   x_2 = 11
   \]

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

   \[
   -4 = \frac{1 + y_2}{2}
   \]

   Multiply both sides by 2:

   \[
   -8 = 1 + y_2
   \]

   Subtract 1 from both sides:

   \[
   y_2 = -9
   \]

### Conclusion:

The coordinates of point \( B \) are \( (11, -9) \).

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

Here are 5 related questions for further exploration:
1. How do you find the midpoint if both points are given?
2. How can you determine the distance between two points?
3. How do you find the equation of a line given two points?
4. What is the significance of the slope of a line segment?
5. How can the midpoint formula be used in geometry problems?

**Tip:** Always double-check your calculations by substituting the values back into the formula to verify your results.

Learn how to find the coordinates of point B given the midpoint M(4, -4) of line AB and the coordinates of point A(-3, 1). This problem covers coordinate geometry concepts and the application of the midpoint formula. Suitable for students in Grades 7-9.

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