Parallel and perpendicular lines in linear functions

Lessons

• Introduction
  a)

  • Definition of Parallel and Perpendicular Lines
  • How does that relate to slope?
  
  

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• 1.
  Determine whether the three points A (-2,-1), B(0,4) & C(2,9) all lie on the same line.

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• 2.
  Determine the following slopes are parallel, perpendicular, or neither.
  i) $m_1 = {2 \over 5}, m_2= {2 \over 5}$
  
  ii) $m_1 = {1 \over5} , m_2 = - {5 \over 1}$
  
  iii) $m_1 = {4 \over 7}, m_2 = {12 \over 21}$
  
  iv) $m_1 =$undefined, $m_2 = 0$
  
  v) $m_1 =mn^{-1}; m_2 =-m^{-1}b$

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• 3.
  Given the points of two lines, determine when the lines are parallel, perpendicular or neither.
  
  a)

  Line 1: (3,2) & (1,4); Line 2: (-1,-2) & (-3,-4)
  
  
  b)

  Line 1: (5,6) & (7,8); Line 2: (-5,-6) & (-7,-8)
  
  
  c)

  Line 1: (0,4) & (-1,2); Line 2: (-3,5) & (1,7)
  
  

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• 4.
  Show that the points A(-3,0), B(1,2) and C(3,-2) are the vertices of a right triangle.

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• 5.
  Show that the points A(-1,-1), B(3,0), C(2,4) and D(-2,3) are the vertices of a square.

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