three vertices of a parallelogram ABCD are A(-2,3) , B(6,7) , C(8,3). Find the fourth vertex D.
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Given that
vertices of parallelogram ABCD
A = (-2,3)
B = (6,7)
C = (8,3)
D = ?
Joining A to C and B to D
we get
Diagonal AC = Diagonal BD
Also mid point O is the center
thus
Coordinated of O According to Diagonal AC
O = [ 3, 3 ]
According to diagonal BD
O = [ 6+x/2, 7+y/2 ]
Thus
6+x/2 = 3
6+x = 6
x = 0
And
7+y/2 = 3
y = -1
Thus
D = (0, -1)
vertices of parallelogram ABCD
A = (-2,3)
B = (6,7)
C = (8,3)
D = ?
Joining A to C and B to D
we get
Diagonal AC = Diagonal BD
Also mid point O is the center
thus
Coordinated of O According to Diagonal AC
O = [ 3, 3 ]
According to diagonal BD
O = [ 6+x/2, 7+y/2 ]
Thus
6+x/2 = 3
6+x = 6
x = 0
And
7+y/2 = 3
y = -1
Thus
D = (0, -1)
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