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 a straight line perpendicular to $2x - 3y + 7 = 0$ forms a triangle with the coordinate axes whose area is $3 \text{ sq. units}$,then the equation of the straight line is:

The area of the triangle bounded by the straight line $ax + by + c = 0$ $(a, b, c \neq 0)$ and the coordinate axes is

Find the incenter of the triangle formed by the axes and the line $\frac{x}{a} + \frac{y}{b} = 1$.

The equation of the base of an equilateral triangle is $x+y=2$ and its opposite vertex is $(2,1)$. If $m_1, m_2$ are the slopes of the other two sides and the length of its side is $a$,then $|m_1-m_2|+a \sqrt{2}=$

Let $ABC$ be a triangle such that the equations of lines $AB$ and $AC$ are $3y-x=2$ and $x+y=2$,respectively,and the points $B$ and $C$ lie on the $x$-axis. If $P$ is the orthocentre of the triangle $ABC$,then the area of the triangle $PBC$ is equal to