Question

The midpoint of AB is M (0, -4). If the coordinates of A are (2, -1), what are the

coordinates of B?

Answer 1

Answer: B(-2,-7)

Explanation:

`\displaystyle\\M(x_M,y_M)=((x_A+x_B)/(2),(y_A+y_B)/(2)) \\\\x_A=2\ \ \ \ x_M=0\ \ \ \ y_A=-1\ \ \ \ y_M=-4\\\\x_M=(x_A+x_B)/(2) \\\\Multiply\ both\ parts\ of \ the \ equation\ by\ 2:\\2x_M=x_A+x_B\\\\\Rightarrow\ x_B=2x_M-x_A\\\Rightarrow \ x_B=2(0)-2\\\Rightarrow\ x_B=0-2\\\Rightarrow\ x_B=-2\\Similarly,\\y_B=2y_M-y_A\\y_B=2(-4)-(-1)1\\y_B=-8+1\\y_B=-7\\Thus,\\B(-2,-7)`