Question

The midpoint of AB is M (2, -7). If the coordinates of A are (-2, -8), what are the coordinates of B?

Answer 1

We have a segment AB, of which we know the coordinates of one endpoint A=(-2,-8) and the midpoint M=(2,-7).

We can relate the x and y coordinates of the endpoints and the midpoints as:

$\begin{gathered} x_M=\frac{x_A+x_B}{2} \\ y_M=\frac{y_A+y_B}{2} \end{gathered}$

The coordinates of the midpoints are the average of the coordinates of the endpoints.

As we know the coordinates of A and M, we can calculate the coordinates of B as:

$\begin{gathered} x_M=\frac{x_A+x_B}{2} \\ 2x_M=x_A+x_B \\ x_B=2x_M-x_A \\ x_B=2\cdot2-(-2)=4+2=6 \end{gathered}$$\begin{gathered} y_B=2\cdot y_M-y_A \\ y_B=2\cdot(-7)-(-8)=-14+8=-6 \end{gathered}$

Answer: the coordinates of B are (6, -6)