Answer :

Given, A quadrilateral has vertices (4, 1), (1, 7), (– 6, 0) and (– 1, – 9).


To Prove: Mid – Points of the quadrilateral form a parallelogram.


The formula used: Mid point formula =


Explanation: Let ABCD is a quadrilateral


E is the midpoint of AB


F is the midpoint of BC


G is the midpoint of CD


H is the midpoint of AD


Now, Find the Coordinates of E, F,G and H using midpoint Formula


Coordinate of E =


Coordinate of F =


Coordinate of G =


Coordinate of H =


Now, EFGH is a parallelogram if the diagonals EG and FH have the same mid – point


Coordinate of mid – point of EG =


Coordinate of mid – point of FH =


Since Diagonals are equals then EFGH is a parallelogram.


Hence, EFGH is a parallelogram.


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