Q. If the points (p, q); (m, n) and (p-m, q-n) are collinear. Show that pn=qm.

Q. If the points (p, q); (m, n) and (p-m, q-n) are collinear. Show tha

1.	Q. If the points (p, q); (m, n) and (p-m, q-n) are collinear. Show that pn=qm.
Answer» Given points are collinear. Therefore[p {tex}\\times{/tex}\xa0n + m(q - n) + (p - m) q] - [m {tex}\\times{/tex}\xa0q + (p - m) n + p (q - n)] = 0{tex}\\Rightarrow{/tex}\xa0(pn + qm - mn + pq - mq) - (mq + pn - mn + pq - pn) = 0{tex}\\Rightarrow{/tex}\xa0(pn + p q - mn) - (mq - mn + pq) = 0{tex}\\Rightarrow{/tex}\xa0pn - mq = 0{tex}\\Rightarrow{/tex}\xa0pn = qm