SOLUTION: I have a parrallelogram with the coordinates E (-1,2) F(2,4) G(7,-1) and H (4,-3) We need to find the coordinates of the bisecting diagonals which they are calling point P

Algebra ->  Parallelograms -> SOLUTION: I have a parrallelogram with the coordinates E (-1,2) F(2,4) G(7,-1) and H (4,-3) We need to find the coordinates of the bisecting diagonals which they are calling point P      Log On


   

Question 477553: I have a parrallelogram with the coordinates E (-1,2) F(2,4) G(7,-1) and H (4,-3)
We need to find the coordinates of the bisecting diagonals which they are calling point P.
We drew out the parallelogram on a grid but we are unsure how to calculate the middle point of the bisecting diagonals. Any help would be greatly appreciated. Thank you for your time.
Debbie
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
You just need the midpoint formula, which just tells us
to average the two x-coordinates and average the two y-coordinates.

In other words, the midpoint between the two points 

%28matrix%281%2C3%2C%0D%0A%0D%0Ax%5B1%5D%2C%22%2C%22%2Cy%5B1%5D%29%29 and %28matrix%281%2C3%2C%0D%0A%0D%0Ax%5B2%5D%2C%22%2C%22%2Cy%5B2%5D%29%29 

is given by 

So to find the midpoint of diagonal EG, it is the midpoint between

%28matrix%281%2C3%2C-1%2C%22%2C%22%2C2%29%29 and %28matrix%281%2C3%2C7%2C%22%2C%22%2C-1%29%29 and is given by

%28matrix%281%2C3%2C%28-1%2B7%29%2F2%2C%22%2C%22%2C+%282%2B%28-1%29%29%2F2%29%29 = %28matrix%281%2C3%2C6%2F2%2C%22%2C%22%2C+1%2F2%29%29 = %28matrix%281%2C3%2C3%2C%22%2C%22%2C1%2F2%29%29.

As a check, also find the midpoint of diagonal FH, which is the midpoint
between %28matrix%281%2C3%2C2%2C%22%2C%22%2C4%29%29 and %28matrix%281%2C3%2C4%2C%22%2C%22%2C-3%29%29 and is given by %28matrix%281%2C3%2C%282%2B4%29%2F2%2C%22%2C%22%2C+%284%2B%28-3%29%29%2F2%29%29 = %28matrix%281%2C3%2C6%2F2%2C%22%2C%22%2C+1%2F2%29%29 = %28matrix%281%2C3%2C3%2C%22%2C%22%2C1%2F2%29%29.

They turn out to be the same point, so %28matrix%281%2C3%2C3%2C%22%2C%22%2C1%2F2%29%29 is the correct midpoint.

Edwin