Question

The midpoint of AB is M(7,-7) if the coordinates of A are (8,-6) what are the coordinates of B

Answer 1

`B(6,-8)`

Explanation:

The first thing is to represent the situation as follows

To calculate the value of B we have the following formula for the midpoint:

`\begin{gathered} (M_1,M_2)=((x_1+x_2)/(2),(y_1+y_2)/(2)) \\ M_1=(x_1+x_2)/(2) \\ M_2=(y_1+y_2)/(2) \end{gathered}`

replacing and solving in each case:

`\begin{gathered} 7=(8+x_2)/(2)\rightarrow x_2=7\cdot2-8\rightarrow x_2=6 \\ -7=(-6+y_2)/(2)\rightarrow y_2=-7\cdot2+8\rightarrow y_2_{}=-8 \\ B(6,-8) \end{gathered}`