Question

If (-2,1) (1,0) and (4,3) are 3 successive vertices of a parallelogram find the fourth vertex

Answer 1

Answer:

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. Therefore (1,2) is the fourth vertex.

Answer 2

Answer:

Diagonal of a parallelogram bisects each other and the point of intersection is M (m, n). Now m = (- 2 +4) /2 = 1 and n = (1 + 3) /2 = 2. Let the coordinate of fourth vertex be D (x, y). Now m = (1 + x) / 2 and n = y /2 or, 1 = (x +1) /2 and 2 = y/2 or, x = 0 and y = 4.

Therefore the coordinate of fourth vertex is (0, 4).