Let $O$ denote the origin. If $M(1, 2)$,$N(0, 1)$,and $A(x, y)$ are points such that $xy > 0$ and $x + y < 1$,then choose the correct statement.

Let the mirror image of point $A(\alpha, \beta)$ in the line mirror $x + 2y = 3$ be point $B$,and the image of $B$ in the line $3x - 2y = 5$ be $C$. If the origin is the orthocentre of triangle $ABC$ and $P(a, b)$ is a point inside the triangle such that triangles $PAB$,$PBC$,and $PCA$ have the same area,then $3(a + b)$ is:

The diagonals $AC$ and $BD$ of a rhombus $ABCD$ intersect at the point $O(3,4)$. If $BD=2 \sqrt{2}$, $A=(1,2)$, $B=(\alpha, \beta)$, $D=(\gamma, \delta)$ and $\alpha < \delta < \gamma < \beta$, then the value of $\beta+\gamma-\delta$ is:

The diagonals of a parallelogram $ABCD$ are along the lines $x+3y=4$ and $6x-2y=7$. Then $ABCD$ must be a

The three points $(-2, 2)$,$(8, -2)$,and $(-4, -3)$ are the vertices of:

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 $\frac{y_1 y_2 y_3 y_4}{x_1 x_2 x_3 x_4}=$