Question

The points (p,q), (m,n),(p-m,q-n) are collinear. To prove:pn= qm

Answer 1

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Answer 2

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$(p, q) (m, n) (p - m, q - n)$

For a co-linear, 

$x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3 (y_1 - y_2) = 0$

$p (n - q + n) + m (q - n - q) + (p - m) (q - n) = 0$

$p (2n - q) + (-mn) + p(q - n) - m(q - n) = 0$

[tex]2pn - pq - mn + pq - pn - qm + mn = 0 [/tex]

After cancellation,

⇒ $pn = qm$