The distance between the point $(2, 1)$ and the image of the point $(3, -1)$ with respect to the line $2x + y - 1 = 0$ is

One vertex of the equilateral triangle with centroid at the origin and one side as $x + y - 2 = 0$ is

Starting from the point $A(-3, 4)$,a moving object touches the line $2x + y - 7 = 0$ at point $B$ and reaches the point $C(0, 1)$. If the object travels along the shortest path,the distance between $A$ and $B$ is:

If $PM$ is the perpendicular from $P(2, 3)$ onto the line $x + y = 3$,then the coordinates of $M$ are

Suppose $A$ and $B$ are two points on the line $2x - y + 3 = 0$ and $P(1, 2)$ is a point such that $PA = PB$. Then,the mid-point of $AB$ is

$A$ straight line $L_1$ passing through $A(3,1)$ meets the coordinate axes at $P$ and $Q$ such that its distance from the origin $O$ is maximum. Then the area of $\triangle OPQ$ is (in sq. units):