Question

Show that points P(2,-2), Q(7,3), R(11,-1) and S (6,-6) are vertices of a parallelogram.

Answer 1

We know one thing about parallelogram,
$\bf{diagonals\:of\:paralllelogram\:bisect\:each\:other}$
e.g., midpoint of diagonal PR = midpoint of diagonal QS

midpoint of diagonal PR = {(2 + 11)/2, (-2 -1)/2 } = (13/2,-3/2)
[ From midpoint section formula, we know that if two points (x₁,y₁) and (x₂,y₂) are given then midpoint of line joining of giebn pouts is {(x₁ + x₂)/2, (y₁ + y₂)/2}]

Similarly, midpoint of QS = {(7 + 6)/2 , (3 -6)/2} = (13/2 , -3/2)
Here we see midpoint of PR = midpoint of QS
so, PQRS is parallelogram