If $ABCD$ is a quadrilateral,and the midpoints of consecutive sides $AB, BC, CD$,and $DA$ are joined by straight lines to form a quadrilateral $PQRS$,then $PQRS$ is always:

If the straight lines $2x + 3y - 1 = 0$,$x + 2y - 1 = 0$,and $ax + by - 1 = 0$ form a triangle with the origin as the orthocentre,then $(a, b)$ is equal to

If the vertices of a triangle have integer coordinates,then what type of triangle can it never be?

$A$ triangle with vertices $(4, 0), (-1, -1), (3, 5)$ is

The points $(1,3)$ and $(5,1)$ are two opposite vertices of a rectangle. The other two vertices lie on the line $y = 2x + c$,where $c$ is a constant. The coordinates of the other two vertices are:

Let a point $A$ lie between the parallel lines $L_1$ and $L_2$ such that its distances from $L_1$ and $L_2$ are $6$ and $3$ units,respectively. Then the area (in sq. units) of the equilateral triangle $ABC$,where the points $B$ and $C$ lie on the lines $L_1$ and $L_2$ respectively,is: