Find the orthocenter of the triangle with vertices $(8, -2)$,$(2, -2)$,and $(8, 6)$.

Two vertices of a triangle are $(5, -1)$ and $(-2, 3)$. If the orthocentre is the origin,then the coordinates of the third vertex are:

Let $A(-3, 2)$ and $B(-2, 1)$ be the vertices of a triangle $ABC$. If the centroid of this triangle lies on the line $3x + 4y + 2 = 0$,then the vertex $C$ lies on the line

Let $k$ be an integer such that the triangle with vertices $(k, -3k)$,$(5, k)$,and $(-k, 2)$ has an area of $28$ sq. units. Then the orthocentre of this triangle is at the point:

If the vertices of a triangle are $(2, 1), (5, 2)$ and $(3, 4)$,then its circumcentre is

$(-2, -1)$ and $(2, 5)$ are two vertices of a triangle and $\left(2, \frac{5}{3}\right)$ is its orthocenter. If $(m, n)$ is the third vertex of that triangle,then $m+n=$