A) Parallelogram
B) Square
C) Rectangle
D) Collinear
Correct Answer: B
Solution :
Let \[A\,(0,\,-1),\,B\,(2,\,\,1),\,\,C\,(0,\,\,3)\] and \[D\,(-2,\,1).\] Obviously\[AB=BC=CD=AD=2\sqrt{2}\] Also, \[AC=BD=4\] and slope of line \[AB=1,\] Slope of line\[AD=-1\]. \[\therefore \,\,\,\angle DAB={{90}^{o}}\] . Similarly, \[\angle B=\angle C=\angle D={{90}^{o}}\] i.e. each angle is right angle. \[\therefore \] Quadrialteral is a square.
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