A) \[\left( 2,\frac{1}{2} \right)\]
B) \[\left( 2,-\frac{1}{2} \right)\]
C) \[\left( 1,\frac{3}{4} \right)\]
D) \[\left( 1,-\frac{3}{4} \right)\]
Correct Answer: A
Solution :
We have \[\frac{1}{2}\left\| \begin{matrix} k & -3k & 1 \\ 5 & k & 1 \\ -k & 2 & 1 \\ \end{matrix} \right\|=28\] \[\Rightarrow \]\[5{{k}^{2}}+13k-46=0\] or \[5{{k}^{2}}+13k+66=0\] (no real solution exist) \[\therefore \] \[k=\frac{-23}{5}\]or \[k=2\] As k is an integer, so k = 2 \[\Rightarrow \] orthocentre is \[\left( 2,\frac{1}{2} \right)\]You need to login to perform this action.
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