Find the possible co-ordinates of the fourth corner of a parallelogram if its three corners are located at (3,3),(4,4), and (2,1).
A
(8,0)
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B
(8,−1)
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C
(−1,9)
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D
(1,0)
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E
(4,−3)
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Solution
The correct option is D(1,0) Let the corners be A(3,3);B(4,4);C(2,1) Let the fourth vertex D =(x,y) We know that the diagonals of a parallelogram bisect each other. So, the midpoint of AC is same as the midpoint of BD.
Mid point of two points (x1,y1) and (x2,y2) is calculated by the formula (x1+x22,y1+y22). So, midpoint of AC= Mid point of BD ⇒(3+22,3+12)=(4+x2,4+y2) ⇒(52,42)=(4+x2,4+y2)