question_answer

A rectangle ABCD has its side AB parallel to line \[y=x\]and vertices A, B and D lie on \[y=1,\] \[x=2\] and \[x=-\,\,2,\]respectively. Locus of vertex C is

A) 3, 7      

B)  5, 5   

C)  6, 4     

D)  8, 9

Correct Answer: B

Solution :

  Let the equation of side AB be \[y=x+a\] Then, \[A\equiv (1-a,1),\]\[B\equiv (2,2+a).\]Equation of side AD is \[y-1=-\,\,(x-(1-a)).\]Hence, \[D\equiv \,\,(-2,4-a).\] Let \[C\equiv \,\,(h,k).\]Then, \[h+1-a=2-2\] \[\Rightarrow \]\[h=a-1\]and \[k+1=2+a+4-a\Rightarrow k=5\] Thus locus of C is y = 5.