Question

If the points (p,q),(m,n)and (p-m,q-n) are collinear show that pn=qn​

Answer 1

`(x_(1),y_(1)), (x_(2), y_(2)), (x_(3) ,y_(3) )` These three points are collinear so if
`x_(1) (y_(2) -y_(3) )+x_(2) (y_(3)- y_(1))+ x_(3) (y_(1) -y_(2))=0`

Since the points (p q) (m n)and (p-m,q-n) are collinear, use the formula to solve the problem.

`p(n-(q-n))+m(q-(n+q))+(p-m)(q-n)=0\\\\p(n-q+n)+m(q-n-q)+(p-m)(q-n)=0\\\\p(2n-q)-mn+(p-m)(q-n)=0\\\\2pn-pq-mn+pq-pn-mq+mn=0\\\\pm-mq=0\\\\pn=mq`

Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! As well as a great Superbowl Weekend! :-)

- Cutiepatutie ☺❀❤