Question

sendo A(-2,3) e B (6,-3) extremidade de um seguimento,determinar os pontos F e G que dividem o seguimento AB em três partes de mesmo comprimento.

Answer 1

 
                     |____________|___________|___________|
                  A(-2,3)           F(xF,yF)         G(xG,yG)           B(6, - 3)
                         AF = FG = GB

         Determinar uma constante para x
                     kx = (xB - xA)/3
                          = [6 - (-2)]/3
                          = 8/3
                                          xF = kx + xA
                                               = 8/3 + (- 2)
                                               = 8/3 - 6/3
                                                                            xF = 2/3
                                         xG = kx + xF
                                                  8/3 + 2/3                          
                                                                            xG = 10/3 
                 F(2/3, 10/3)

    Constante para y
                      ky = (- 3 - 3)/3
                           = - 2
                                           yF = 3 + (-2)
                                                                            yF = 1
                                          yG = 1 - 2
                                                                            yG = - 1
                 G(1, - 1)