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Perpendicular Lines 10.
A (4, 4) D (-4, 4) B (4, -4) C (-4, -4) 90 0 90 0
Perpendicular Lines 0 y x A (a , b) B (-b , a) After a 90 0  rotation  (anti-clockwise) A moves to B As both lines go through origin gradients are: 90 0 NB Fraction has been turned upside down and turned into negative
Copy the following: For perpendicular lines: 1. Lines are perpendicular 2. To find gradient of line perpendicular to given line think: “ Flip the fraction and change the sign”
Example 1 What is the gradient of a line perpendicular to the line through the points P (4 , 7) and Q (5 , 11) ? Solution : ,[object Object],[object Object],Flip fraction- change sign 2.  Use m 1  x m 2  = -1 to find gradient of perpendicular line.
Example 2 Two lines have equations  3x + 2y - 7 = 0  &  4x - 6y + 1 = 0 Prove that they are perpendicular. Solution : ,[object Object],[object Object],[object Object],Line 1 3x + 2y - 7 = 0 2y = -3x + 7 Gradient 1 = -3/2   Line 2 4x - 6y + 1 = 0 6y = 4x + 1 Gradient 2 =  2/3 2.  Find the gradient of line 2 by rearranging and using y = mx + c
Example 2 Two lines have equations  3x + 2y - 7 = 0  &  4x - 6y + 1 = 0 Prove that they are perpendicular. Solution : 3.  Check that m 1  x m 2  = -1 4.  Make statement Since  m 1  x m 2  = -1 lines are perpendicular
Heinemann, p.6, Ex 1D, Q1, 2, 3 & 6

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10 Perpendicular Lines

  • 2. A (4, 4) D (-4, 4) B (4, -4) C (-4, -4) 90 0 90 0
  • 3. Perpendicular Lines 0 y x A (a , b) B (-b , a) After a 90 0 rotation (anti-clockwise) A moves to B As both lines go through origin gradients are: 90 0 NB Fraction has been turned upside down and turned into negative
  • 4. Copy the following: For perpendicular lines: 1. Lines are perpendicular 2. To find gradient of line perpendicular to given line think: “ Flip the fraction and change the sign”
  • 5.
  • 6.
  • 7. Example 2 Two lines have equations 3x + 2y - 7 = 0 & 4x - 6y + 1 = 0 Prove that they are perpendicular. Solution : 3. Check that m 1 x m 2 = -1 4. Make statement Since m 1 x m 2 = -1 lines are perpendicular
  • 8. Heinemann, p.6, Ex 1D, Q1, 2, 3 & 6