The image of the point $(3,5)$ in the line $x-y+1=0$ lies on:

If the family of straight lines $ax + by + c = 0$,where $2a + 3b = 4c$,is concurrent at the point $P(l, m)$,then the foot of the perpendicular drawn from $P$ to the line $x + y + 1 = 0$ is

If a particle moving along $x-2y-3=0$ gets reflected in a perpendicular direction upon hitting the line $3x-2y-5=0$,then the line of the movement of the particle after reflection 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:

Consider the lines $x(3 \lambda+1)+y(7 \lambda+2)=17 \lambda+5$,where $\lambda$ is a parameter. All these lines pass through a fixed point $P$. One of these lines (say $L$) is farthest from the origin. If the distance of $L$ from the point $(3,6)$ is $d$,then the value of $d^2$ is

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