Question

If three vertices of a parallelogram are a(1,1), b(4,4) and c(4,8). Find the fourth vertex d

Answer 1

Let A(1, 1), B(4, 4) and D(xLet A(1, 1), B(4, 4), C(4, 8) and D(x, y) be the vertices of a parallelogram ABCD taken in order. Since, the diagonals of a parallelogram bisect each other.Therefore coordinates of the mid-point of AC = Coordinates of the mid-point
of BD.

(1+4/2 , 1+4/2) = (4+x/2 , 8+y/2) 

(5/2 , 5/2) = (4+x/2 , 8+y/2) 

4 + x = 5 , 8 + y = 5

x = 1 ,  y = -3 

Therefore (1, -3) is the fourth vertex.