Endpoints of segment MN have coordinates (0, −3), (−2, −4). Endpoints of segment AB have coordinates (2, 5), (4, k). What value of k makes these segments perpendicular?

Answer:The answer to your question is: k = 1Step-by-step explanation:DataMN    (0, -3)  ,  (-2, -4)AB     (2, 5)   ,  (4 , k)Formula  [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]ProcessSlope MN = [tex]\frac{-4 + 3}{-2 + 0}[/tex]   = [tex]\frac{1}{2}[/tex]Slope AB = [tex]\frac{k - 5}{4 - 2}  = \frac{k - 5}{2}[/tex]If the lines are perpendicular then,                   [tex]- 2 = \frac{k - 5}{2}[/tex]                   -4 = k - 5                  k = -4 + 5                  k = 1