Question

As coordenadas do ponto médio de um segmento AB, são (3,-1). Sabendo que as coordenadas do ponto B são (8,4). Determine as coordenadas do ponto A.

Answer 1

$\boxed{P_m(\frac{x_a+x_b}{2}\ ,\ \frac{y_a+y_b}{2})}$

$P_m = (3,-1)$

$P_m_x = \frac{x_a+x_b}{2}\\\\ 3 = \frac{x_a+8}{2}\\\\ 6 = x_a+8\\\\\ \boxed{x_a=-2}$

$P_m_y = \frac{y_a+y_b}{2}\\\\\ -1 = \frac{y_a+4}{2}\\\\\ -2 = y_a+4\\\\\ \boxed{y_a=-6}$

$\boxed{A(-2,-6)}$