(Q21) Show that the points A(7,3) B(6,1) C(8,2) and D(9,4) taken in that order are vertices of parallelogram .

Answer

Let the points A(7,3) B(6,1) C(8,2) and D(9,4) are vertices of a parallelogram.

So the mid point of the diagonal AC and DB should be same

A(7,3)B(6,1)C(8,2)D(9,4)
Now we find the mid point of AC and DB by using (
x1+x2
2
 ,
y1+y2
2
) formula
midpoint of AC = (
+
2
 ,
+
2
)= (
2
 ,
2
)
Mid point of DB = (
+
2
 ,
+
2
) = (
2
 ,
2
)

Hence mid point of AC and midpoint of DB is same.

Therefore, the point A,B,C,D are vertices of a parallelogram.