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If the points (p,q) (m,n)and (p-m)(q-n)are …

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If the points (p,q) (m,n)and (p-m)(q-n)are collinear ,then prove that pn-qm

Posted by Sidharth Rana 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Given points are collinear. Therefore

[p {tex}\times{/tex} n + m(q - n) + (p - m) q] - [m {tex}\times{/tex} q + (p - m) n + p (q - n)] = 0
{tex}\Rightarrow{/tex} (pn + qm - mn + pq - mq) - (mq + pn - mn + pq - pn) = 0
{tex}\Rightarrow{/tex} (pn + p q - mn) - (mq - mn + pq) = 0
{tex}\Rightarrow{/tex} pn - mq = 0
{tex}\Rightarrow{/tex} pn = qm

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