Question

The midpoint of AB is M(-6, 4), If the coordinates of A are (-7, 2), what are the coordinates of B?

Answer 1

The coordinates of B are (-5, 6)

Step-by-step explanation:

The midpoint of AB with coordinates:

`\begin{gathered} (x_1,y_1),(x_2,y_2) \\ \end{gathered}`

is given as:

`M((x_1+x_2)/(2),(y_1+y_2)/(2))`

Since the coordinate of A are (-7, 2), we have:

`M((-7+x_2)/(2),(2+y_2)/(2))=M(-6,4)`
`\begin{gathered} (-7+x_2)/(2)=-6 \\ \\ -7+x_2=-12 \\ \\ x_2=-5 \end{gathered}`
`\begin{gathered} (2+y_2)/(2)=4 \\ \\ 2+y_2=8 \\ \\ y_2=6 \end{gathered}`

Therefore, the coordinates of B are (-5, 6)