Three consecutive vertices of a parallelogram are (-2,-1),(1,0),(4,3).Find fourth vertex?

Three consecutive vertices of a parallelogram are (-2,-1),(1,0),(4,3).

1.	Three consecutive vertices of a parallelogram are (-2,-1),(1,0),(4,3).Find fourth vertex?
Answer» Let A(-2, -l), B(1, 0). C(4, 3) 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.(-2+4/2, -1+3/2) = (1+x/2, 0+y/2)(1,1) = (1+x/2 , y/2)x+1 = 2, y=2Therefore (1,2) is the fourth vertex. fourth vertex is (1,2)