Question

show that the points (p,q) (m,n) and (p-m,q-n) are collinear ,determine the relation between p,q,and m

Answer 1

this is just a example

Let A(p,q) B(m,n) and C(p-m,q-n), then,

 If the points are collinear, than, area of  tri. ABC = 0

so, 1/2{p(n-(q-n) +m(q-n-q) + (p-m)(q-n)}

  =  1/2{p(2n-q) -mn +pq -pn -mq +mn

0 = 2pn -pq -mn +pq -pn -qm +mn

so,  qm = 2pn - pn

so, qm = pn.....proved..

I hope this will help you