Question

Se M (3,2) é o ponto médio entre A(1,3) e b então determine as coordenadas do ponto b

Answer 1

$M~=~Pt.~Medio~de~\overline{AB}\\\\\\M~=~\left(\frac{x_A+x_B}{2}~,~\frac{y_A+y_B}{2}\right)\\\\\\Substituindo~os~dados:\\\\\\(3~,~2)~=~\left(\frac{1+x_B}{2}~,~\frac{3+y_B}{2}\right)\\\\\\Igualando~coordenada~a~coordenada:\\\\\\\frac{1+x_B}{2}~=~3\\\\\\1+x_B~=~2~.~3\\\\\\x_B~=~6-1\\\\\\\boxed{x_B~=~5}\\\\\\\\\frac{3+y_B}{2}~=~2\\\\\\3+y_B~=~2~.~2\\\\\\y_B~=~4-3\\\\\\\boxed{y_B~=~1}$

Resposta: As coordenadas do ponto B são (x,y) = (5 , 1)