Question

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

Answer 1

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Answer 2

Answer:

Since, Three points $(x_1,y_1)$ , $(x_2,y_2)$. $(x_3,y_3)$ are called col-linear if,

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

Thus, If the points (p q) (m n)and (p-m,q-n)are col-linear,

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

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

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

$\implies 2pn-pq-mn+pq-pn-mq+mn=0$

$\implies pn - mq = 0$

$\implies pn = mq$

Hence, proved.