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We are given the following information:

- The midpoint \( M(1, 3) \)
- Point \( A(3, 1) \)
- We need to find the coordinates of point \( B \).

The formula for the midpoint between two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is:

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

Substitute the known values of \( M \) and \( A \):

\[
(1, 3) = \left( \frac{3 + x_2}{2}, \frac{1 + y_2}{2} \right)
\]

This gives two equations:

1. \( \frac{3 + x_2}{2} = 1 \)
2. \( \frac{1 + y_2}{2} = 3 \)

Solve each equation:

### For \( x_2 \):
\[
\frac{3 + x_2}{2} = 1
\]
Multiply both sides by 2:
\[
3 + x_2 = 2
\]
Subtract 3 from both sides:
\[
x_2 = -1
\]

### For \( y_2 \):
\[
\frac{1 + y_2}{2} = 3
\]
Multiply both sides by 2:
\[
1 + y_2 = 6
\]
Subtract 1 from both sides:
\[
y_2 = 5
\]

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

Would you like further details or have any questions? Here are some related questions:

1. How can the midpoint formula be derived from geometry?
2. What is the distance between points \( A \) and \( B \)?
3. How would the solution change if the midpoint was given in 3D space?
4. What are some real-life applications of midpoint calculations?
5. How can the midpoint be used to divide a line segment in a different ratio?

**Tip:** When solving for an unknown in midpoint problems, always work with each coordinate (x and y) separately.

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

Learn how to find the coordinates of point B when given the midpoint M(1, 3) and point A(3, 1) using the midpoint formula. This problem explores key concepts in coordinate geometry and algebra, suitable for students in Grades 7-9.

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