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 ☺❀❤