If the vertices of a triangle are $(0, 4)$,$(4, 1)$,and $(7, 5)$,find its perimeter.

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

If the sum of the distances of a point from two perpendicular lines in a plane is $1$,then its locus is

The equation of one side of an equilateral triangle is $x+y=2$ and one vertex is $(2,-1)$. The length of the side is

If the equations of three sides of a triangle are $x = 2$,$y + 1 = 0$,and $x + 2y = 4$,then the coordinates of the circumcentre of this triangle are:

Let $A(1,2)$ and $C(-3,-6)$ be two diagonally opposite vertices of a rhombus, whose sides $AD$ and $BC$ are parallel to the line $7x-y=14$. If $B(\alpha, \beta)$ and $D(\gamma, \delta)$ are the other two vertices, then $|\alpha+\beta+\gamma+\delta|$ is equal to: