The midpoint of start overline, AB, end overline 
AB
  is M, left parenthesis, minus, 2, comma, 4, right parenthesisM(−2,4). If the coordinates of AA are left parenthesis, minus, 1, comma, 6, right parenthesis(−1,6), what are the coordinates of BB?

To find the coordinates of \( B \), we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint \( M \) of a line segment with endpoints \( A(x_1, y_1) \) and \( B(x_2, y_2) \) are given by:

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

### Given:
- Midpoint \( M(-2, 4) \)
- Coordinates of \( A(-1, 6) \)
- Coordinates of \( B(x_2, y_2) \) are unknown.

### Step 1: Write midpoint equations
\[
-2 = \frac{-1 + x_2}{2} \quad \text{(for the x-coordinate)}
\]
\[
4 = \frac{6 + y_2}{2} \quad \text{(for the y-coordinate)}
\]

### Step 2: Solve for \( x_2 \)
Multiply both sides of the x-coordinate equation by 2:
\[
-4 = -1 + x_2
\]
\[
x_2 = -4 + 1 = -3
\]

### Step 3: Solve for \( y_2 \)
Multiply both sides of the y-coordinate equation by 2:
\[
8 = 6 + y_2
\]
\[
y_2 = 8 - 6 = 2
\]

### Final Answer:
The coordinates of \( B \) are:
\[
B(-3, 2)
\]

Let me know if you'd like a detailed breakdown or have further questions! 😊  
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### Relative Questions:
1. How do you verify the midpoint of a line segment?
2. What are some applications of the midpoint formula in geometry?
3. Can the midpoint formula be extended to three dimensions? How?
4. What if \( A \) and \( B \) were both variables? How would you solve for the midpoint?
5. How can you use the midpoint formula to find the equation of the perpendicular bisector?

### Tip:
Always double-check your arithmetic when solving midpoint problems to avoid errors in simple addition or subtraction.

The midpoint of segment AB is M(-2, 4). If the coordinates of A are (-1, 6), what are the coordinates of B?

Learn how to determine the coordinates of point B when given the midpoint and one endpoint of a line segment. This problem uses the midpoint formula, focusing on coordinate geometry concepts, and is suitable for Grades 6-8 students.

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