Question

The midpoint of AB is M(4, -2). If the coordinates of A are (3, -6), what are thecoordinates of B?

Answer 1

In general, given two points, the midpoint between those two points is given by the formula below

`\begin{gathered} (x_1,y_1),(x_2,y_2) \\ \Rightarrow midpoint=((x_1+x_2)/(2),(y_1+y_2)/(2)) \end{gathered}`

Therefore, in our case, if B=(x,y),

`\begin{gathered} (4,-2)=((3+x)/(2),(-6+y)/(2)) \\ \Rightarrow4=(3+x)/(2) \\ and \\ -2=(-6+y)/(2) \\ \Rightarrow8=3+x \\ and \\ -4=-6+y \\ \Rightarrow x=5 \\ and \\ y=2 \end{gathered}`
`\Rightarrow B=(5,2)`

Therefore, the answer is B=(5,2)