A, B, C have the vertices such as (-3,2), (1,5) and (2,-4) respectively. Let the coordinates of D be (x,y)
Now, diagonals of parallelogram bisects each other equally.
Let the diagonals bisects at m.
therefore, taking diagonal AC,
m(x, y) = (x₁+x₂)/2, (y₁+y₂)/2 = (-3+2)/2, (2-4)/2 = -1/2, -1
Now taking BD as diagonal,
mx = (1+x)/2 => -1/2 = (1+x)/2 => -1 = 1+x => x = -2
and, my = (5+y)/2 => -1 = (5+y)/2 => -2 = 5+y => y = -7
Hence, the coordinates of D is (-2, -7)
