Question

Determinar la ecuación de la recta, en forma general, que pasa por el punto medio del
segmento definido por los puntos A( −5,2 ) y B( 5,3 ) y es perpendicular a dicho segmento

Answer 1

Ecuación explícita de la recta
             y = ax + b
                   a = pendiente = (y2 - y1)/(x2 -x1)
                   b = ordenada en el origen
RECTA AB
                      a = (3 - 2)/[5 - (-5)]
                         = 1/10
   En B(5, 3)
                     3 = (1/10).5 + b
                        = 1/2 + b
              3 - 1/2 = b
                      b = 5/2
                                                   recta
                                                              y = (1/10)x + 5/2

RECTA PERPENDICULAR
         a = - 1/(1/10)                       punto medio recta AB
            = -10                                [(- 5 + 5)/2, (2 + 3)/2]
                                                         Pm(0, 5/2)

                        En Pm(0, 5/2)
                                               5/2 = (- 10).0 + b
                                                  b = 5/2

                                                                  ECUACIÓN
                                                             y = - 10x + 5/2   explícita
                                                     todo x2
                                                             2y = - 20x + 5
                                                             - 20x - 2y + 5 = 0  general