Question

The points (3, -4) and (-6, 2) are the extremities of a diagonal of a parallelogram. If the third vertex is (-1, -3), find the co-ordinates of the fourth vertex..

Answer 1

Answer:

Fourth vertex of parallelogram is (-2, 1).

Step-by-step explanation:

Let A(3, -4) and C(-6, 2) be the extremities of diagonal AC and B(-1,-3), D(x, y) the extremities of diagonal BD. Since the diagonals of a parallelogram bisect each other. Therefore, Coordinates of mid-point of AC = Coordinates of mid point of BD.                                                                                                                3-6/2 = x-1/2 -> -3/2 = x-1/2 -> x = -2.                                                                                      And, -4+2/2 = y-3/2 -> -2/2 = y-3/2 -> y = 1.                                                                     Hence, the fourth vertex of parallelogram is (-2, 1).