The midpoint of start overline, AB, end overline
AB
is M, left parenthesis, minus, 1, comma, 6, right parenthesisM(−1,6). If the coordinates of AA are left parenthesis, minus, 5, comma, 7, right parenthesis(−5,7), what are the coordinates of BB?

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

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

Given:
- \( M(-1, 6) \)
- \( A(-5, 7) \)
- We need to find \( B(x_2, y_2) \).

Using the midpoint formula, we can set up the following equations:

\[
-1 = \frac{-5 + x_2}{2}
\]
\[
6 = \frac{7 + y_2}{2}
\]

### Solving for \( x_2 \):

\[
-1 = \frac{-5 + x_2}{2}
\]

Multiply both sides by 2:

\[
-2 = -5 + x_2
\]

Add 5 to both sides:

\[
x_2 = 3
\]

### Solving for \( y_2 \):

\[
6 = \frac{7 + y_2}{2}
\]

Multiply both sides by 2:

\[
12 = 7 + y_2
\]

Subtract 7 from both sides:

\[
y_2 = 5
\]

### Coordinates of Point \( B \):
So, the coordinates of point \( B \) are \( (3, 5) \).

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the midpoint formula for a 3-dimensional space?
2. How do you find the distance between two points in a plane?
3. What are the coordinates of a point that divides a line segment in a given ratio?
4. How can you verify if a point lies on a given line segment?
5. How does the slope of a line relate to the coordinates of its endpoints?

**Tip:** Always check your final answer by substituting it back into the original equation or formula to ensure accuracy.

The midpoint of AB is M(-1, 6). If the coordinates of A are (-5, 7), what are the coordinates of B?

Learn how to find the coordinates of point B given the midpoint M(-1, 6) and point A(-5, 7). This problem involves the midpoint formula and is suitable for students in Grades 7-9.

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