Geometry: How to determine if lines are parallel or perpendicular

So let say you have a lines in a graph,

to determine if these are perpendicular, they must have relevant values which the first line's slope must be the reciprocal of the other line intersecting the first line.

Below is an example of determining a parallel lines.

L₁ = {-1, -2} and {1, 2}
L₂ = {2, 0} and {0, 4}

To solve the slopes,

m1 = 2-(-2)/1- (-1)
      = 2+2/ 1+1
      = 4/2
      = 2

m2 = 4 - 0/ 0 - (-2)
      = 4/2
      = 2


since they are both identical then this lines are both parallel.

For perpendicular lines,


L₁ = {0, -4} and {-1, -7}
L₂ = {3, 0} and {-3, 2}


m1 = -7 - (-4)/ -1 -0
      = -7 + 4/ -1
      = -3/-1
      = 3

m2  = 2 - 0 /-3 - (3)
       = 2 / -6
       = - 1/3

so m1 and m2 slopes have the reciprocal values. No matter where do we start on measuring, still, perpinduclar lines will result to reciprocal values and perpendicular lines have an "angle of 90 degrees".


This page can be a great reference to look at http://www.purplemath.com/modules/slope2.htm