A) Square
B) Parallelogram
C) Rectangle
D) Rhombus
Correct Answer: B
Solution :
Let \[A\,(-1,\,\,1),\,\,B\,(0,\,\,-3),\,\,C\,(5,\,\,2)\] and \[D\,(4,\,\,6)\] \[\Rightarrow \,\,AB=\sqrt{17},\,\,CD=\sqrt{17},\,\,BC=\sqrt{50},\,\] \[AD=\sqrt{50,}\,\,AC=\sqrt{37}\] and \[BD=\sqrt{97}\] Obviously, \[zx+3y=9\] and \[2{{x}_{1}}+3{{y}_{1}}=9\] Also diagonal \[AC\ne BD.\] Therefore, quadrilateral is parallelogram.
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