The orthocentre of the triangle whose vertices are $(0, 0)$,$(3, 0)$,and $(0, 4)$ is

If $(a, b - c)$,$(b, c - a)$,and $(c, a - b)$ are the vertices of a triangle,then where does the centroid of the triangle lie?

Find the incenter of the triangle with vertices $(1, \sqrt{3})$,$(0, 0)$,and $(2, 0)$.

$(-2, -1)$ 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 $m+n=$

The quadratic equation whose roots are the coordinates of the circumcentre of the triangle formed by the points $(-2,-1), (6,-1),$ and $(2,5)$ is

If the vertices $P, Q, R$ of a triangle $PQR$ are rational points,which of the following points of the triangle $PQR$ is (are) always a rational point $(s)$? ($A$ rational point is a point both of whose coordinates are rational numbers.)