Q. 54.3( 13 Votes )

Prove that when the point s A (7, 3), B (9, 6), C (10, 12) and D (8, 9) are joined in order, then they will form a parallelogram.

Answer :

We know that a quadrilateral is a parallelogram if the co-ordinates of mid-point s of its both the diagonals are same.

Therefore, we’ll find the mid-point s of diagonal AC and BD.


Let the co-ordinates of mid-point of AC be (x3, y3).


And, we know mid-point formula, i.e. the coordinates of mid-point of line joining (x1, y1) and (x2, y2) is




(Where, (x1, y1) and (x2, y2) are the coordinates of A and C




Co – ordinates of mid-point of AC =


Now, Let the co-ordinates of mid-point of BD be (x4, y4).


And, since it is a mid-point –



(Where, (x5, y5) and (x6, y6) are the coordinates of B and D.




Co – ordinates of mid-point of BD =


And, since these are equal –


ABCD is a parallelogram.


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