Theorem 3.6: The shortest distance from a point to a line is the perpendicular distance.

 

Proof: Let   P   be a point not on the line, and let   F   be its foot in the line. Let   A   be any other point on the line.

Let

a = |PF|

b = |FA|

c = |PA|

Then by the Pythagorean theorem, Theorem 3.4,

next theorem (3.7)