Question

The midpoint of \overline{\text{AB}}

AB
is M(1, -3)M(1,−3). If the coordinates of AA are (4, -7)(4,−7), what are the coordinates of BB?

Answer 1

`~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{4}~,~\stackrel{y_1}{-7})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +4}{2}~~~ ,~~~ \cfrac{ y -7}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M} }{(1~~,~~-3)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +4 }{2}=1\implies x+4=2\implies \boxed{x=-2} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -7 }{2}=-3\implies y-7=-6\implies \boxed{y=1}`