If the coordinates of the points $A,\, B,\, C$ be $(-1, 5),\, (0, 0)$ and $(2, 2)$ respectively and $D$ be the middle point of $BC$, then the equation of the perpendicular drawn from $B$ to the line $AD$ is
$x + 2y = 0$
$2x + y = 0$
$x - 2y = 0$
$2x - y = 0$
The base of an equilateral triangle with side $2 a$ lies along the $y$ -axis such that the mid-point of the base is at the origin. Find vertices of the triangle.
Co-ordinates of the orthocentre of the triangle whose vertices are $A(0, 0) , B(3, 4)$ and $C(4, 0)$ is
$A(-1, 1)$, $B(5, 3)$ are opposite vertices of a square in $xy$-plane. The equation of the other diagonal (not passing through $(A, B)$ of the square is given by
Given three points $P, Q, R$ with $P(5, 3)$ and $R$ lies on the $x-$ axis. If equation of $RQ$ is $x - 2y = 2$ and $PQ$ is parallel to the $x-$ axis, then the centroid of $\Delta PQR$ lies on the line