Question

Points p,q , m,n and p-m,q-n are collinear. Prove that pn=qm.

Answer 1

Use area of the triangle=0

Answer 2

Since they are collinear
x1(y2-y3)+x2 (y3-y1)+x3 (y1-y2)=0
p(n-q+n)+m(q-n-q)+p-m (q-n)
p (2n-q)+m (-n)+p-m (q-n)=0
2np-pq-mn+pq-pn-qm +mn=0
np -qm =0
np=qm