A) \[(-1,-1)\]
B) \[(2,2)\]
C) \[(-2,-2)\]
D) None of these
Correct Answer: C
Solution :
Let the co-ordinate of vertex A be\[(h,k)\]. Then \[AD\]is perpendicular to \[BC\], therefore \[OA\,\bot \,BC\] Þ \[\frac{k-0}{h-0}\times \frac{-1}{1}=-1\Rightarrow k=h\] .....(i) Let the coordinates of D be\[(\alpha ,\beta )\]. Then the co-ordinates of O are \[\left( \frac{2\alpha +h}{2+1},\frac{2\beta +k}{2+1} \right)\]. Therefore \[\frac{2\alpha +h}{3}=0\] and \[\frac{2\beta +k}{3}=0\] \[\Rightarrow \alpha =-\frac{h}{2},\beta =\frac{-k}{2}\]. Since \[(\alpha ,\beta )\]lies on \[x+y-2=0\]Þ\[\alpha +\beta -2=0\] Þ \[-h/2-k/2-2=0\]Þ\[h+k+4=0\] Þ \[2h+4=0\Rightarrow h=k=-2\], [from (i)] Hence the coordinates of vertex A are\[(-2,-2)\].You need to login to perform this action.
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