The area of a parallelogram formed by the lines $ax \pm by \pm c = 0$ is

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

The circumcentre of the triangle formed by the lines $x = -2$,$y = -2$ and $x + y + 2 = 0$ is

If the points $(a, b)$,$(a', b')$ and $(a - a', b - b')$ are collinear,then:

$A$ regular octagon is formed by cutting congruent isosceles right-angled triangles from the corners of a square. If the square has side length $1$,the side length of the octagon is

$A$ rectangle $ABCD$ has its side parallel to the line $y=2x$ and vertices $A, B, D$ are on lines $y=1, x=1$ and $x=-1$ respectively. The coordinate of $C$ can be