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, 5, comma, 4, right parenthesis(5,4), what are the coordinates of BB?

To find the coordinates of point \( B \), we can use the midpoint formula. The midpoint \( M(x_m, y_m) \) 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:
- The midpoint \( M(-1, 6) \)
- The coordinates of \( A(5, 4) \)

We need to find the coordinates of \( B(x_2, y_2) \).

### Step 1: Set up the equations

Using the midpoint formula, we have:

\[
-1 = \frac{5 + x_2}{2} \quad \text{and} \quad 6 = \frac{4 + y_2}{2}
\]

### Step 2: Solve for \( x_2 \)

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

Multiply both sides by 2:

\[
-2 = 5 + x_2
\]

Subtract 5 from both sides:

\[
x_2 = -7
\]

### Step 3: Solve for \( y_2 \)

\[
6 = \frac{4 + y_2}{2}
\]

Multiply both sides by 2:

\[
12 = 4 + y_2
\]

Subtract 4 from both sides:

\[
y_2 = 8
\]

### Final Answer
The coordinates of point \( B \) are \( (-7, 8) \).

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How is the midpoint formula derived?
2. What are other ways to find the distance between two points?
3. How can you check if three points are collinear using their coordinates?
4. What is the significance of the midpoint in geometry?
5. How can the midpoint formula be applied in real-world problems?

**Tip:** When working with coordinates, always double-check the signs to avoid errors in calculations!

The midpoint of line segment AB is M(-1, 6). If the coordinates of A are (5, 4), what are the coordinates of B?

Learn how to determine the coordinates of point B when given the midpoint M(-1, 6) and point A(5, 4) using the midpoint formula. This problem is a key concept in coordinate geometry, suitable for students in Grades 6-8.

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