Question

As coordenadas do ponto médio de um segmento AB são M(-1,2). Sabendo-se que as coordenadas do ponto A são (2,5), então, determine as coordenadas de B. 

Answer 1

$x_M=\frac{x_A+x_B}{2}\\ \\ -1=\frac{2+x_B}{2}\\ \\ 2+x_B=-2\\ \\ \boxed{x_B=-4}$

$y_M=\frac{y_A+y_B}{2}\\ \\ 2=\frac{5+y_B}{2}\\ \\ 5+y_B=4\\ \\ \boxed{y_B=-1}$

Answer 2

$Pm = ( \frac{x1 + x2}{2}, \frac{x1 + x2}{2}) = (-1,2)\\\\ \frac{x1 + x2}{2} = -1\\\\ x1 + x2 = -2\\\\ 2 + x2 = -2\\\\ \boxed{x2 = -4}\\\\ \frac{y1 + y2}{2} = 2\\\\ y1 + y2 = 4\\\\ 5 + y2 = 4\\\\ \boxed{y2 = -1}\\\\ \boxed{AB = (x2,y2) = (-4,-1)}$