Question

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

Answer 1

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.

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



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



Since both the coordinates are of the same point O,