If $Q$ is the image of the point $P(1,1)$ with respect to the straight line $x+y+1=0$,then the length of the perpendicular drawn from $Q$ to the line $3x-4y+3=0$ is

The coordinates of the foot of the perpendicular from the point $(2, 3)$ on the line $y = 3x + 4$ are given by

If the foot of the perpendicular drawn from the origin to a straight line is $(3, -4)$,then the equation of the line is:

From the point $(-1, -1)$, two rays are sent making angles of $45^\circ$ with the line $x+y=0$. These rays get reflected from the mirror $x+2y=1$. If the equations of the reflected rays are $ax+by=9$ and $cx+dy=7$, where $a, b, c, d \in Z$, then the value of $ad+bc$ is . . . . . . .

If the image of point $P(\lambda, 2\lambda)$ in the line mirror $x - y + 2 = 0$ is $Q(\mu, 3\lambda)$,then choose the correct option.

If $A$ and $B$ are two points on the line $3x + 4y + 15 = 0$ such that $OA = OB = 9$ units,then the area of the triangle $OAB$ is