If the vertices $P$ and $Q$ of a triangle $PQR$ are given by $(2, 5)$ and $(4, -11)$ respectively, and the point $R$ moves along the line $N: 9x + 7y + 4 = 0$, then the locus of the centroid of the triangle $PQR$ is a straight line parallel to

A variable straight line passes through a fixed point $(a, b)$ intersecting the co-ordinates axes at $A\,\, \&\,\, B$. If $'O'$ is the origin then the locus of the centroid of the triangle $OAB$ is :

If two vertices of a triangle are $(5, -1)$ and $( - 2, 3)$ and its orthocentre is at $(0, 0)$, then the third vertex

The origin and the points where the line $L_1$ intersect the $x$ -axis and $y$ -axis are vertices of right angled triangle $T$ whose area is $8$. Also the line $L_1$ is perpendicular to line $L_2$ : $4x -y = 3$, then perimeter of triangle $T$ is -

Let $PQR$ be a right angled isosceles triangle, right angled at $P\, (2, 1)$. If the equation of the line $QR$ is $2x + y = 3$, then the equation representing the pair of lines $PQ$ and $PR$ is

One diagonal of a square is along the line $8x - 15y = 0$ and one of its vertex is $(1, 2)$ Then the equation of the sides of the square passing through this vertex, are