Answer: A
Let \(H(h,k)\) be orthocentre.\(\Rightarrow(\)slopes of \(AH).(\)slope of \(BC)\)
\(\displaystyle\Rightarrow \left( \dfrac { k-\dfrac { 16 }{ 7 } }{ h+\dfrac { 3 }{ 7 } } \right) .\left( -1 \right) =-1\)
\(\displaystyle\Rightarrow k-\frac { 16 }{ 7 } =h+\frac { 3 }{ 7 } \)
\(\displaystyle\Rightarrow h-k=-\frac { 19 }{ 7 } \) ...(i)
Also, \((\)slope of \(CH).(\)slopes of \(AB)=-1\)
\(\displaystyle\Rightarrow \frac { k-4 }{ h+3 } .\left( 4 \right) =-1\Rightarrow 4k-16=-h-3\)
\(\displaystyle\Rightarrow h+4k=13\) ...(ii)