Question

Prove that the points $(a,b),(c,d)$ and $(a-c,b-d)$ are collinear, if $ad=bc$.

Answer 1

If points are collinear, then area=0

$or\left(\frac{1}{2}\right)\left[a\right(d-b+d)-b(c-a+c)+1(cb-cd-ad+cd\left)\right]=0a(2d-b)-b(2c-a)+(cd-ad)=02ad-ab-2bc+ab+cb-ad=0ad-bc=0orad=bcrequiredcondition.$