First we must locate point B as it is vital to finding the midpoint of BD. To do this, we take the average of the endpoints AC since B is its midpoint.
x values = -9 + 1 = -8 Then divide by 2 for the average -8/2 = -4
y values = -4 + 6 = 2 Then divide by 2 for the average 2/2 = 1
Therefore B must be (-4, 1)
Now we know the values of E must be the average of B and D. So we can write equations for each coordinate since we know they are averages.
x - values = (Bx + Dx)/2 = Ex (-4 + Dx)/2 = -4 ---> multiply both sides by 2 -4 + Dx = -8 ---> add -4 to both sides Dx = -4
y - values = (By + Dy)/2 = Ey (1 + Dy)/2 = -3 ---> multiply both sides by 2 1 + Dy = -6 ---> subtract 1 from both side Dy = -7
