If in a parallelogram $ABDC$, the coordinates of $A, B$ and $C$ are respectively $(1, 2), (3, 4)$ and $(2, 5)$, then the equation of the diagonal $AD$ is

In a rectangle $A B C D$, the coordinates of $A$ and $B$ are $(1,2)$ and $(3,6)$ respectively and some diameter of the circumscribing circle of $A B C D$ has equation $2 x-y+4=0$. Then, the area of the rectangle is

The diagonal passing through origin of a quadrilateral formed by $x = 0,\;y = 0,\;x + y = 1$ and $6x + y = 3,$ is

One side of a square is inclined at an acute angle $\alpha$ with the positive $x-$axis, and one of its extremities is at the origin. If the remaining three vertices of the square lie above the $x-$axis and the side of a square is $4$, then the equation of the diagonal of the square which is not passing through the origin is

The triangle formed by the lines $x + y - 4 = 0,\,$ $3x + y = 4,$ $x + 3y = 4$ is

Two vertices of a triangle are $(5, - 1)$ and $( - 2,3)$. If orthocentre is the origin then coordinates of the third vertex are