the coordinates of \( B \) are \( (3,1) \).
The coordinates of the midpoint \( M \) between points \( A \) and \( B \) can be found using the midpoint formula:
\[ M\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \]
Given that the coordinates of \( M \) are \( (1,2) \) and the coordinates of \( A \) are \( (-1,3) \), we can use this information to find the coordinates of \( B \). Let the coordinates of \( B \) be \( (x, y) \).
Using the midpoint formula:
\[ 1 = \frac{(-1 + x)}{2} \]
\[ 2 = \frac{(3 + y)}{2} \]
Solving these equations:
For the first equation:
\[ -1 + x = 2 \]
\[ x = 3 \]
For the second equation:
\[ 3 + y = 4 \]
\[ y = 1 \]
Therefore, the coordinates of \( B \) are \( (3,1) \).