Question

If (1, 2), (4, y), ( x, 6) and (3, 5) 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 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
$(\frac{1+x}{2},\frac{2+6}{2})\Rightarrow (frac1+x2,4)$
If O is the mid-point of BD, then the coordinates of O are
$(\frac{4+3}{2},\frac{5+y}{2})\Rightarrow (\frac{7}{2},\frac{5+y}{2})$
Since bothe the coordinates are of the same point O,
$\therefore frac1+x2=frac72and4=frac5+y2$
$\Rightarrow x+1=7and5+y=8$
$\Rightarrow x=6andy=3$