The midpoint of start overline, AB, end overline 
AB
  is M, left parenthesis, minus, 3, comma, 4, right parenthesisM(−3,4). If the coordinates of AA are left parenthesis, minus, 5, comma, 1, right parenthesis(−5,1), what are the coordinates of BB?

To find the coordinates of point \( B \) given the midpoint \( M \) and the coordinates of point \( A \), we can use the midpoint formula.

### 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 calculated as:
\[
x_m = \frac{x_1 + x_2}{2}, \quad y_m = \frac{y_1 + y_2}{2}
\]

Given:
- Midpoint \( M = (-3, 4) \)
- Coordinates of \( A = (-5, 1) \)

Let the coordinates of \( B \) be \( (x_2, y_2) \).

### Finding Coordinates of \( B \)

1. **Find \( x_2 \):**

\[
-3 = \frac{-5 + x_2}{2}
\]

Multiply both sides by 2:

\[
-6 = -5 + x_2
\]

Solve for \( x_2 \):

\[
x_2 = -6 + 5 = -1
\]

2. **Find \( y_2 \):**

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

Multiply both sides by 2:

\[
8 = 1 + y_2
\]

Solve for \( y_2 \):

\[
y_2 = 8 - 1 = 7
\]

### Coordinates of \( B \)

The coordinates of point \( B \) are:

\[
B(-1, 7)
\]

Would you like more details on how to solve this or have any other questions?

Here are 5 related questions you might find interesting:

1. How do you find the distance between two points in a coordinate plane?
2. What is the formula for the slope of a line segment between two points?
3. How do you find the equation of a line given two points?
4. What is the reflection of a point across the origin?
5. How do you determine if three points are collinear?

**Tip:** Always double-check your calculations when solving for coordinates to avoid simple mistakes.

The midpoint of segment AB is M(-3, 4). If the coordinates of A are (-5, 1), what are the coordinates of B?

Learn how to find the coordinates of point B when given the midpoint M(-3,4) and the coordinates of point A(-5,1) using the midpoint formula. This problem covers key concepts in coordinate geometry, suitable for students in Grades 8-10.

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