The coordinates of E is ( w+v, u)
A parallelogram is a polygon with four sides, it has two pairs of parallel sides.
The diagonals of a parallelogram bisect each other.
A parallelogram CDEF in a coordinate plane is shown.
The coordinates of point C is (-v,0)
The coordinates of point D is (w,0)
The coordinates of point F is (0,u)
The coordinates of point E has to be determined.
From the property of the parallelogram
The diagonals DF and CE bisect each other.
The midpoint of DF and the midpoint of CE will have the same coordinates.
The coordinates of the midpoint of DF is given by,
( (x₁+x₂)/2, (y₁+y₂)/2)
= (w/2 , u/2 )
The coordinates of midpoint of CE is also (w/2 , u/2 )
(w/2 , u/2 ) = ( (-v +x₂)/2, (0+y₂)/2 )
w/2 = -v +x₂/2
x₂ = w+v
u/2 = 0+y₂/2
y₂ = u
The coordinates of E is ( w+v, u)
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