Question

If the points (p, q), (m, n) and (p - m, q -n) are colliear, show that pn = qm.​

Answer 1

If the three points are collinear, it means that their slope is 0.
Formula for slope:
(y₂-y₁)/(x₂-x₁)

First taking the slope of points (p,q) and (m,n) and then the slope of points (m,n) and (p-m,q-n) which is both equal to 0 and hence equal.
Therefore, (n-q)/(m-p)=(q-n-n)/(p-m-m)
or, (n-q)/(m-p)=(q-2n)/(p-2m)
or, (n-q)(p-2n)=(q-2n)(m-p)
or, pn-pq-2mn+2qm=qm-pq-2mn+2pn
or, pn-pq+pq-2mn+2mn+2qm=qm+2pn
or, 2pn-pn=2qm-qm
or, pn=qm