Question

M is the midpoint of segment AB. M is located at (3, 10) and A is located at (-5, 7).What are the coordinates of B?

Answer 1

(-1,13)

1) Let's find the Coordinates of B, using the Midpoint Formula for that:

`M=((x_A+x_B)/(2),(y_A+y_B)/(2))`

2) Plugging into that the given information:

`\begin{gathered} M=((x_A+x_B)/(2),(y_A+y_B)/(2)) \\ (3,10)=(\frac{-5_{}+x_B}{2},\frac{7_{}+y_B}{2}) \\ \\ \frac{-5+x_B_{}}{2}=-3 \\ -5+x_B=-6 \\ x_B=-6+5 \\ x_B=-1 \\ \frac{7_{}+y_B}{2}=10 \\ 7+y_B=20 \\ y_B=20-7 \\ y_B=13 \end{gathered}`

3) Hence, the coordinates of point B are (-1,13)