The coordinates of G is (d+c, b)
This is because the opposite sides of any parallelogram are equal in length, and so the length of side HG is equal to the length of side EF.
a) The length of side HG is equal to the horizontal distance (x2 - x1): xG - 0
The length of side EF is equal to the horizontal distance (x2 - x1): d - (-c) = d +c
Thus:
xG - 0 = d + c
xG = d + c
Therefore the x-coordinate of G is d + c
b) To find the y-coordinate of G, we also apply the idea that sides GF and HE are equal.
The length of side GF is equal to the vertical distance (y2 - y1): yG - 0
The length of side HE is equal to the vertical distance (y2 - y1): b - 0
Thus:
yG - 0 = b -0
yG = b
Therefore the y-coordinate of G is b
Finally, the coordinates of G is (xG, yG) = (d+c, b)