Question

Two verticies of paralellogram ABCD are A(-6,-1) and B(-5,3). The intersection of the diagonals, E, are (-2, 1/2). Determine the coordinates of D.

Answer 1

The diagonals bisect each other so (-2, 1/2) is the midpoint of both.
So use the midpoint theorem
let (a,b) be the point opposing A(-6,-1)
then (-6+a)/2 = -2
-6+a = -4
a = 2
and
(-1+b)/2 = 1/2
-1+b = 1
b = 2
So the point opposite A is (2,2)

Find the other point in the same way

Answer 2

The diagonals bisect each other, so E is the midpoint of BD.
So, D is just as far from E as E is from B
E-B = (4,3/2)
So, D = E + (4,3/2) = (-2,1/2)+(4,3/2) = (2,2)

Answer 3

Oops. I also found C. I said BE, but actually used AE.
But you can find D in the same way.