Method to find the distance from the point P(0,3) to the line y=-3x.
 
  • Find any 2 points on the line:

For example A(0,0) and B(2,-6)

  • Find the components of the vector AB and its orthogonal complement u.
AB<2,-6>. Its orthogonal complement u is  <6,2>.
  • Find the components of AP.
AP<0,3>
  • The distance is the scalar projection of AP on u.
d=AP.u/|u|=3√(10)/10
Copyright 2012-2015, Dr. Fanny Dos Reis