Question

The midpoint of start overline, AB, end overline

AB
is M, left bracket, 1, comma, 2, right bracketM(1,2). If the coordinates of AA are left bracket, minus, 1, comma, 3, right bracket(−1,3), what are the coordinates of BB?

Answer 1

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 \( (3,1) \).