SOLUTION: A(-2,1) B(4,4) O (0,0) AOBE is a parallelogram. Find the co-ordinates of E. The gradients are the same, right?

Algebra ->  Expressions -> SOLUTION: A(-2,1) B(4,4) O (0,0) AOBE is a parallelogram. Find the co-ordinates of E. The gradients are the same, right?      Log On


   

Question 1043165: A(-2,1) B(4,4) O (0,0)
AOBE is a parallelogram. Find the co-ordinates of E.
The gradients are the same, right?
Found 2 solutions by Fombitz, Edwin McCravy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Not sure what you mean about gradients being the same.
So going from A to O would be the same procedure as going from E to B.
Similarly, going from O to B would be the same procedure as going from A to E.
So starting with O and going to B, you move 4 units right, 4 units up.
B:(0,0)+(4,4)=(4,4)
So starting with A, move 4 units right, 4 units up to find E.
E:(-2,1)+(4,4)=(2,5)
As a check, going from A to O, move 2 units right, 1 unit down,
O:(-2,1)+(2,-1)=(0,0)
So then moving from E to B should also be the same,
B: (2,5)+(2,-1)=(4,4)
So we're consistent
E: (2,5)

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!


To get from O to A, we go LEFT 2 and UP 1.
See the green lines above.

Therefore to get from B to E, we do the same.
Going LEFT 2 and UP 1 from B, puts us here:

 

and we see that the point is E(2,5), so we
finish drawing parallelogram AOBE:



Edwin