Question

The midpoint of AB is M(-5, -2). If the coordinates of A are (-3, 4), what arethe coordinates of B?

Answer 1

The midpoint formula to find the midpoint coordintaes of line AB is

$\begin{gathered} (x,y)=\frac{x_1+x_2}{2},\text{ }\frac{y_1+y_2}{2} \\ \text{where (x,y) is the coordinates of midpoint M, (x}_1,y_1)\text{ is coordinates of A} \\ x_2,y_2\text{ are coordinates of B} \end{gathered}$

Substitute

$\begin{gathered} (-3,4)for(x_1,y_1)\text{ and }(-5,\text{ -2) for }(x,y) \\ -5=\frac{-3+x_2}{2} \\ -5\ast2=-3+x_2 \\ -10+3=x_2 \\ x_2=-7 \\ \text{for y coordinate of }B \\ -2=\frac{4+y_2}{2} \\ -2\ast2=4+y_2 \\ -4=4+y_2 \\ -4-4=y_2 \\ y_2=-8 \end{gathered}$

Thus, the coordinates of B is (x2,y,2)=(-7,-8)