Question

The co-ordinates of three vertices of a parallelogram are (2,3), (-5,-7) and (2,-4), Find the co-ordinates of fourth vertex.

Answer 1

Let the parallelogram be ABCD, having co-ordinates of A, Band C as (2,3), (-5-7) and (2,-4) respectively and let (x,y) be the co-ordinates of fourth vertex D. We know that the diagonals of parallelogram bisect each other (say at point P)

Therefore P is the mid point of AC as well as that of BD.

or, -5+x = 4 and -7+y = -1

or, x = 9 and y = 6

so, Co-ordinates of Dare (9,6)