A line makes intercepts 5 and 7 on the coordinate axes. The axes are rotated through an angle $\theta$ in the positive direction about the origin so that the line makes equal intercepts on the new axes, then $|\tan \theta|=$

$L \equiv 7 x-y+8=0$ is one of the diagonals of a square for which $(-4,5)$ and $(3,4)$ are two vertices. Then, the coordinates of the two vertices lying on the diagonal $L=0$ are

The locus of the image of a variable point $(\alpha, 2 \alpha-1)$ with respect to the line $3 x-2 y+4=0$, is

Let $M$ be the foot of the perpendicular drawn from the point $(5,-7)$ to the line $3 x-5 y+1=0$. Then, the perpendicular distance from $M$ to the line $2 x+5 y-3=0$ is