The four points whose coordinates are $(2, 1), (1, 4), (4, 5), (5, 2)$ form:

The equation of the base $BC$ of an equilateral triangle is $3x + 4y = 1$ and the vertex $A$ is $(-3, 2)$. Then the area of the triangle is-

In a triangle $ABC$,if $BC=5, CA=6, AB=7$,then the length of the median drawn from $B$ onto $AC$ is

If a diagonal of a square is along the line $8x - 15y = 0$ and one of its vertices is $(1, 2)$,then the equations of the sides of the square passing through this vertex are

The centre of a square of side $4$ units length is $(3,7)$ and one of the diagonals is parallel to the line $y=x$. If $(x_1, y_1), (x_2, y_2), (x_3, y_3)$ and $(x_4, y_4)$ are the vertices of this square,then $\frac{y_1 y_2 y_3 y_4}{x_1 x_2 x_3 x_4}=$

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