(Q31)Prove that the points (-7,-3) , (5,10) , (15,8) and (3,-5) taken in order are the corners of a parallelogram.

To show that the given points form a parallelogram

We have to show that the mid points of each diagonal are same. Since diagonals of a parallelogram bisect each other

Now Let A(-7,-3) , B(5,10) , C(15,8) , and D(3, -5)

Then mid point of diagonal

AC = (
-+
2
 ,
-+
2
 )
= (
2
 ,
2
 ) = ( ,
2
 ) --------------(1)

And now midpoint of diagonal

BD = (
+
2
 ,
-
2
 )
= (
2
 ,
2
 ) = (,
2
 ) --------------(2)

(1)=(2)

Hence the given are vertices of a parallelogram.