Let $PS$ be the median of the triangle with vertices $P(2,\;2),\;Q(6,\; - \;1)$ and $R(7,\;3)$. The equation of the line passing through $(1, -1)$ and parallel to $PS$ is

Area of the rhombus bounded by the four lines, $ax \pm by \pm c = 0$ is :

If the coordinates of the vertices of the triangle $ABC$ be $(-1, 6)$, $(-3, -9)$, and $(5, -8)$ respectively, then the equation of the median through $C$ is

The co-ordinates of the orthocentre of the triangle bounded by the lines, $4x - 7y + 10 = 0; x + y=5$ and $7x + 4y = 15$ is :

The base of an equilateral triangle is along the line given by $3x + 4y\,= 9$. If a vertex of the triangle is $(1, 2)$, then the length of a side of the triangle is

A point $P$ moves on the line $2x -3y + 4 = 0$. If $Q(1, 4)$ and $R(3, -2)$ are fixed points, then the locus of the centroid of $\Delta PQR$ is a line