The midpoint of start overline, AB, end overlineAB is M, left parenthesis, 5, comma, minus, 3, right parenthesis*M*(5,−3). If the coordinates of A*A* are left parenthesis, 3, comma, minus, 8, right parenthesis(3,−8), what are the coordinates of B*B*?

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 \( M(5, -3) \)
- The coordinates of point \( A(3, -8) \)

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

### Step 1: Set up the midpoint equations

\[
5 = \frac{3 + x_2}{2}
\]
\[
-3 = \frac{-8 + y_2}{2}
\]

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

Multiply both sides of the first equation by 2 to eliminate the fraction:

\[
10 = 3 + x_2
\]

Subtract 3 from both sides:

\[
x_2 = 7
\]

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

Multiply both sides of the second equation by 2 to eliminate the fraction:

\[
-6 = -8 + y_2
\]

Add 8 to both sides:

\[
y_2 = 2
\]

### Final Answer:
The coordinates of point \( B \) are \( \boxed{(7, 2)} \).

Do you want details or have any questions?

Here are 5 related questions:
1. How do you find the midpoint if you know the coordinates of both endpoints?
2. What happens if the coordinates of both points are negative in the midpoint formula?
3. How can the midpoint formula be applied to three-dimensional coordinates?
4. How does the distance formula relate to the midpoint formula?
5. What are some real-world applications of the midpoint formula?

**Tip:** Always verify your solution by plugging the coordinates back into the midpoint formula to ensure accuracy.

Learn how to find the coordinates of point B using the midpoint formula. Given the midpoint M(5, -3) and the coordinates of point A(3, -8), this problem covers coordinate geometry concepts. Suitable for students in Grades 7-9.

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