$\text{ If a triangle }ABC\text{ has vertices }A(-1,7),B(-7,1),C(5,-5)\text{ then its orthocentre has coordinates: }$

$\text{ Vertices of the given triangle are }A(-1,7),B(-7,1),C(5,-5)$

$\text{ Observing the points, the vertices are at equal distances from origin, so that the circumcentre of the }$

$\text{ triangle is }S(0,0)$

The centroid of the triangle is 

$\begin{array}{c}G=\left(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}\right)\\ =\left(\frac{-1-7+5}{3},\frac{7+1-5}{3}\right)\\ =\left(-1,1\right)\end{array}$

$\text{ In any triangle }G\text{ divides }OS\text{ in the ratio }2:1\text{ internally }$

It implies 

$O=3G-2S=\boxed{\left(-3,3\right)}$