Question 835146: The diagonals of quadrilateral EFGH intersect at D(-1,4). Two vertices of EFGH are E(2,7) and F(-3,5). What must be the coordinates of G and H to ensure that EFGH is a parallelogram?
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website! 
Since the diagonals of a parallelogram bisect each other we know
that ED is half a diagonal. So we draw in half-diagonal ED.
Going from E to D is going left 3 units and down 3 units, so to
extend the half diagonal to finish the full diagonal EG, from D we go
left 3 units and down 3 units, and arrive at (-4,1), and label it G.
Then we draw side FG
We could finish by doing the same with the other diagonal.
But we can also just realize that going from F to E is
going right 5 units and up 2 units. So to find the point H,
from G we go right 5 units and up 2 units, and arrive at
(1,3), and label it H. Then we draw sides GH and HE.
So G is (-4,1) and H is (1,3)
Edwin
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