The midpoint of start overline, AB, end overline 
AB
  is M, left parenthesis, 3, comma, minus, 4, right parenthesisM(3,−4). If the coordinates of AA are left parenthesis, 7, comma, minus, 3, right parenthesis(7,−3), 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:
- \( M(3, -4) \) is the midpoint.
- \( A(7, -3) \) are the coordinates of point \( A \).

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

### Solving for \( x_2 \):

The \( x \)-coordinate of the midpoint is given by:

\[
3 = \frac{7 + x_2}{2}
\]

Multiply both sides by 2:

\[
6 = 7 + x_2
\]

Subtract 7 from both sides:

\[
x_2 = -1
\]

### Solving for \( y_2 \):

The \( y \)-coordinate of the midpoint is given by:

\[
-4 = \frac{-3 + y_2}{2}
\]

Multiply both sides by 2:

\[
-8 = -3 + y_2
\]

Add 3 to both sides:

\[
y_2 = -5
\]

### Final Answer:

The coordinates of point \( B \) are \( (-1, -5) \).

Would you like more details or have any questions?

Here are five related questions:
1. How do you find the midpoint if the coordinates of \( A \) and \( B \) are both unknown?
2. What is the formula for the distance between two points in a coordinate plane?
3. How would you calculate the coordinates of \( A \) if the coordinates of \( B \) and \( M \) were given?
4. Can the midpoint formula be used in three-dimensional space? How would that formula look?
5. How does the midpoint relate to the concept of the centroid in a triangle?

**Tip:** When dealing with midpoints, always double-check your arithmetic operations to ensure accuracy in finding the unknown coordinates.

The midpoint of AB is M(3,−4). If the coordinates of A are (7,−3), what are the coordinates of B?

Learn how to determine the coordinates of point B using the midpoint formula when given M(3,-4) and A(7,-3). This problem focuses on key concepts in coordinate geometry and is suitable for students in Grades 8-10.

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