Soit (x,y)!=(0,0).

(x',y') colinéaire à (x,y)
<=>
(x',y')=a(x,y)
<=>
x'=ax
y'=ay

1. => xy'-x'y=xay-axy=0

2. <= si x!=0: y'=x'y/x, pose a=x'/x; si y!=0: x'=xy'/y, pose a=y'/y <= xy'-x'y=0