SOLUTION: show that the diagonals of a parellelogram with vertices (-1,1), (0,-3), (3,5)and (4,1) bisect each other show that the diagonals of a parellelogram with vertices (1,-3), (-3,

Algebra ->  Parallelograms -> SOLUTION: show that the diagonals of a parellelogram with vertices (-1,1), (0,-3), (3,5)and (4,1) bisect each other show that the diagonals of a parellelogram with vertices (1,-3), (-3,      Log On


   

Question 536171: show that the diagonals of a parellelogram with vertices (-1,1), (0,-3), (3,5)and (4,1) bisect each other

show that the diagonals of a parellelogram with vertices (1,-3), (-3,-1), (3,5)and (-5,-9) bisect each other
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

We just need to show that the midpoint of each diagonal is the same point.

We find the midpoint of the diagonal connecting (-1,1) and (4,1)

Midpoint = 

Midpoint = %28matrix%281%2C3%2C++++++%28-1%2B4%29%2F2%2C+++%22%2C%22%2C+%281%2B1%29%2F2%29%29 

Midpoint = %28matrix%281%2C3%2C++++++3%2F2%2C+++%22%2C%22%2C+2%2F2%29%29 

Midpoint = %28matrix%281%2C3%2C++++++3%2F2%2C+++%22%2C%22%2C+1%29%29  



We find the midpoint of the diagonal connecting (0,-3) and (3,5)

Midpoint = 

Midpoint = %28matrix%281%2C3%2C++++++%280%2B3%29%2F2%2C+++%22%2C%22%2C+%28-3%2B5%29%2F2%29%29 

Midpoint = %28matrix%281%2C3%2C++++++3%2F2%2C+++%22%2C%22%2C+2%2F2%29%29 

Midpoint = %28matrix%281%2C3%2C++++++3%2F2%2C+++%22%2C%22%2C+1%29%29

Since the two diagonals have the same midpoint, they bisect each other.

Edwin