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

Answer :

Mid point of AC = Mid point BD
$$\Rightarrow \frac{x+1}{2} , \frac{6+2}{2} = \frac{4+3}{2} , \frac{y+5}{2}$$
$$\Rightarrow \frac{x+1}{2} = \frac{7}{2}$$
$$\Rightarrow x +1 = 7$$
$$\Rightarrow x = 7-1= 6$$
$$\Rightarrow \frac{y+5}{2} = \frac{8}{2}$$
$$\Rightarrow y+5 = 8$$
$$\Rightarrow y = 8 -5 = 3$$