Consider the triangle with the given information,

The slope of $AB=0$, so the equation of altitude from $C$ is $x=4$
The slope of $BC=-4$, so the equation of altitude from $A$ is $x-4y+3=0$

Solving these two equations, we get, 
orthocentre of the triangle is $\left(4,\frac{7}{4}\right)$