The midpoint of start overline, AB, end overline 
AB
  is M, left parenthesis, minus, 6, comma, 3, right parenthesisM(−6,3). If the coordinates of AA are left parenthesis, minus, 5, comma, 5, right parenthesis(−5,5), what are the coordinates of BB?

To find the coordinates of point \( B \), we use the midpoint formula. The formula for the midpoint \( M \) of a line segment between points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is:

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

Here, you are given:

- The coordinates of point \( A(-5, 5) \),
- The midpoint \( M(-6, 3) \),
- The coordinates of point \( B(x_2, y_2) \), which are unknown.

Now, let's apply the midpoint formula component-wise.

### 1. For the \( x \)-coordinate:

\[
\frac{-5 + x_2}{2} = -6
\]

Solve for \( x_2 \):

\[
-5 + x_2 = -12 \quad \Rightarrow \quad x_2 = -12 + 5 = -7
\]

### 2. For the \( y \)-coordinate:

\[
\frac{5 + y_2}{2} = 3
\]

Solve for \( y_2 \):

\[
5 + y_2 = 6 \quad \Rightarrow \quad y_2 = 6 - 5 = 1
\]

### Conclusion:

The coordinates of point \( B \) are \( (-7, 1) \).

---

Do you want details on how this formula works, or have any questions?

Here are some related questions:

1. How do you find the distance between points \( A \) and \( B \)?
2. Can you explain how to generalize the midpoint formula for 3D space?
3. If the midpoint and point \( B \) were known, how would you find point \( A \)?
4. How does the midpoint formula relate to vectors?
5. What is the relationship between the midpoint and the centroid of a triangle?

**Tip**: Always check your solutions by substituting back into the formula to confirm!

The midpoint of segment AB is M(-6, 3). If the coordinates of A are (-5, 5), what are the coordinates of B?

Discover how to find the coordinates of point B given the midpoint M(-6, 3) and point A(-5, 5). This problem focuses on coordinate geometry and uses the midpoint formula step-by-step. Suitable for students in Grades 8-10.

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