If $(\alpha, \beta)$ is the orthocentre of the triangle $ABC$ with vertices $A(3, -7)$,$B(-1, 2)$,and $C(4, 5)$,then $9\alpha - 6\beta + 60$ is equal to:

If the midpoints of the sides of a triangle are $(5, 0)$,$(5, 12)$,and $(0, 12)$,then what is the orthocenter of this triangle?

If the equations of the perpendicular bisectors of the sides $AB$ and $AC$ of a $\triangle ABC$ are $x-y+5=0$ and $x+2y=0$ respectively,and if $A$ is $(1,-2)$,then the equation of the perpendicular bisector of the side $BC$ is

If a triangle $ABC$ has vertices $A(1, -6)$, $B(2, -3)$ and $C(3, -2)$, then the coordinates of its orthocenter are....

In the triangle $ABC$ with vertices $A(2, 3)$,$B(4, -1)$ and $C(1, 2)$,find the equation and length of the altitude from the vertex $A$.

Let $A(0,0), B(3,0), C(0,-4)$ be the vertices of $\triangle ABC$. Then the coordinates of the incentre of $\triangle ABC$ are: