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Determine if lines passing through the points are Parallel,perpendicular,or neither line 1:(-2,2)and (2,-4) line 2:(3,6) and (5,3)

Respuesta :

You can tell if two lines are parallel, perpendicular, or neither by looking at their slopes [tex]m_1 [/tex] and [tex] m_2 [/tex]:

  • If [tex] m_1=m_2 [/tex], i.e. if the two lines have the same slope, the lines are parallel
  • If [tex] m_1\cdot m_2=-1 [/tex], the lines are perpendicular
  • In all other cases, the lines are not parallel nor perpendicular.

Given two points [tex] A = (x_A,y_A),\ B = (x_B,y_B) [/tex] of a line, the slope is defined as the ratio between the y and x variation:

[tex]m = \dfrac{\Delta y}{\Delta x} = \dfrac{y_B-y_A}{x_B-x_A} [/tex]

So in this case, we have

[tex] m_1 = \dfrac{2-(-4)}{-2-2} = \dfrac{6}{-4} = -\dfrac{3}{2} [/tex]

[tex] m_2 = \dfrac{3-6}{5-3} = \dfrac{-3}{2} = -\dfrac{3}{2} [/tex]

Since the two slopes are the same, the two lines are parallel.

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