Distance from point to line

For a line and point :

• has direction vector
• Let be the point where makes a right angle to
• We need to find so that
• For and to be perpendicular:
  • $(4\lambda+4\lambda+\lambda)+2+2=0
• We’ve found !
• The perpendicular distance is of length :

Find the distance between the point and the line

• The line has direction vector
• Let be the point where makes a right angle to
• We need to find so that
• For and to be perpendicular:
• We’ve found !
• The perpendicular distance is of length :
• So the distance from the point to the line is .