Math - Coordinate Geometry

• Tullia

  7 Nov 11, 11:15

  The points A,B,C,D have coordinates (1,7), (5,-1), (8,3), (6,7) respectively.
  
  a) Show that AB and CD are parallel.
  
  M1=M2 when parallel. 
  Grad = (y2-y1)/(x2-x1) 
  M1 = (-1-7)/(5-1) = -8/4 = -2/1 = -2 M2 = (7-3)/(6-8) = 4/-2 = -2/1 = -2
  
  -2=-2, therefore M1=M2, therefore AB & CD are parallel.
  
  b) Find the equation of AB.
  
  Equation of a line = (y-y1) = M(x-x1)
  (y--1)=-2(x-5), so y+1=10-2x, so y=9-2x
  
  c) The line L passes through the point D and is perpendicular to AB. Show that L has equation:
  x-2y+8=0
  
  M1 x M2 = -1 or M2 = -1/M1 
  M2 = 1/2
  
  x=0 , so 8-2y=0 , therefore y=4
  y=0 , so x+8=0 , therefore x= -8
  
  Grad = (difference in y)/(difference in x) = (0-4)/0-8) = -1/2
  
  

  Is this correct? I should be getting 1/2 shouldn't I? Please, I've completed the other parts to this question and they're correct but I'm struggled here as I've done what I feel I should be doing but I've got -1/2 rather than 1/2

• FireIce

  7 Nov 11, 12:16

  x - 2y + 8 = 0
  
  (change into y = mx + c) ---> 2y = x + 8

  y = x/2 + 4

   

  so grad = 1/2