Q. 64.2( 323 Votes )

If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

Answer :

Let (1, 2), (4, y), (x, 6), and (3, 5) are the coordinates of A, B, C, D vertices of a parallelogram ABCD.

Intersection point O of diagonal AC and BD also divides these diagonals.

Therefore, O is the mid-point of AC and BD.



By mid point formula, If (x, y) is the midpoint of the line joining points A(x1, y1) and B(x2, y2) Then,

If O is the mid-point of AC, then the coordinates of O are:


() = (, 4)


If O is the mid-point of BD, then the coordinates of O are:


(, ) = (, )


Since both the coordinates are of the same point O

Comparing the x coordinates we get,


x + 1 = 7


x = 6


And,

Comparing the y coordinates we get,

= 4


5 + y = 8


y = 3
Hence, x = 6 and y = 3.

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