Q. 213.7( 3 Votes )

Prove that the points (3, 2), (6, 3), (7, 6), (4, 5) are the vertices of a parallelogram. Is it a rectangle?

Answer :

Given points are A(3, 2), B(6, 3), C(7, 6) and D(4, 5).



We need to prove that these are the vertices of a parallelogram.


We know that in the lengths of opposite sides are equal in a parallelogram.


Let us find the lengths of the sides.


We know that the distance between the points (x1, y1) and (x2, y2) is .


Now,





AB = √10





BC = √10





CD = √10





DA = √10


We got AB = CD and BC = DA, these are the vertices of a parallelogram.


Now we find the lengths of the diagonals.





AC = √32





BD = √8


We got AC≠BD.


The points doesn’t form a rectangle.


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