If the lines $x + 3y = 4$ and $6x - 2y = 7$ are the diagonals of a parallelogram $PQRS$,then $PQRS$ is a:

If the points $(a, 0)$,$(0, b)$,and $(1, 1)$ are collinear,then:

In the given figure,$AB = 12 \, cm$,$CD = 8 \, cm$,$BD = 20 \, cm$,and $\angle ABD = \angle AEC = \angle EDC = 90^{\circ}$. If $BE = x$,then:

If the points $(1, 1)$,$(-1, -1)$ and $(-\sqrt{3}, k)$ are vertices of an equilateral triangle,then the value of $k$ will be:

The points $(1,3)$ and $(5,1)$ are opposite vertices of a diagonal of a rectangle. If the other two vertices lie on the line $y=2x+c$,then one of the vertices on the other diagonal is

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