If $P(2, 2)$,$Q(-2, 4)$,and $R(3, 4)$ are the vertices of $\triangle PQR$,then the equation of the median through vertex $R$ is $........$

The mid-point of the line segment joining the centroid and the orthocentre of the triangle whose vertices are $(a, b), (a, c)$ and $(d, c)$ is

The orthocenter of the triangle whose sides are given by $x+y+10=0$,$x-y-2=0$,and $2x+y-7=0$ is

The base of an equilateral triangle with side $2a$ lies along the $y$-axis such that the mid-point of the base is at the origin. Find the vertices of the triangle.

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:

If in triangle $ABC$,$A \equiv (1, 10)$,circumcentre $\equiv \left( -\frac{1}{3}, \frac{2}{3} \right)$ and orthocentre $\equiv \left( \frac{11}{3}, \frac{4}{3} \right)$,then the coordinates of the mid-point of the side opposite to $A$ are: