One of the vertices of a square is the origin,and the adjacent sides of the square lie along the positive $x$ and $y$ axes. If the side length is $5$,which of the following is $NOT$ a vertex of the square?

The area of the triangle formed by the lines $7x - 2y + 10 = 0$,$7x + 2y - 10 = 0$ and $y + 2 = 0$ is ............ $sq. \, units$.

$A$ square of side length $a$ has one vertex at the origin and one side along the $x$-axis. The side passing through the origin makes an angle $\alpha$ $(0 < \alpha < \pi/4)$ with the positive $x$-axis. Find the equation of the diagonal that does not pass through the origin.

If the points $(k, 3), (2, k),$ and $(-k, 3)$ are collinear,then the values of $k$ are

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

Suppose $ABCD$ $(AB \parallel CD)$ is a trapezium such that the diagonals $AC$ and $BD$ bisect the angles $\angle DAB$ and $\angle CBA$,respectively. Then