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.
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 OComparing the x coordinates we get,
x + 1 = 7
x = 6
And,Comparing the y coordinates we get,
5 + y = 8
y = 3
Hence, x = 6 and y = 3.
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