Question

the point (p, q), (m, n) and (p-m, q-n) are collinear. prove that pn=pm.

Answer 1

Hey...!!!

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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 Ans.

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