Prove that the diagonals of the parallelogram formed by the four lines `3x + y = 0, 3y + x = 0, 3x + y = 4, 3y + x = 4` are at right angles.

Prove that the diagonals of the parallelogram formed by the four lines : x/a +y/b=1,x/b+y/a= 1, x/a + y/b = -1 and x/b + y/a = -1 are at right angles .

Prove that the diagonals of the parallelogram formed by the lines sqrt(3)x+y=0, sqrt(3) y+x=0, sqrt(3) x+y=1 and sqrt(3) y+x=1 are at right angles.

Prove that the diagonals of the parallelogram formed by the lines sqrt(3)x+y=0, sqrt(3) y+x=0, sqrt(3) x+y=1 and sqrt(3) y+x=1 are at right angles.

Prove that the diagonals of the parallelogram formed by the four straight lines : sqrt3x+y=0, sqrt3y+x=0 , sqrt3x+y=1 and sqrt3y+x+1 are at right angle to one another.

Area of the parallelograms formed by the lines 4 y - 3 x-a=0, 3 y-4 x+a =0 4 y-3 x-3 a=0,3 y-4 x+2 a=0

Find the orthocenter of the triangle formed by the lines x + 2y = 0, 4x + 3y - 5 =0, 3x + y = 0 .

The area of the parallelogram formed by the lines 4y-3x-a=0, 3y-4x+a=0, 4y-3x-3a=0, 3y-4x+2a=0 is

The triangle formed by the lines x + y = 0,3x + y = 4,x+3y = 4 is

Prove that the area of the parallelogram formed by the lines 3x-4y+a=0,\ 3x-4y+3a=0,\ 4x-3y-a=0 and 4x-3y-2a=0 is (2a^2)/7 sq. units

Prove that the area of the parallelogram formed by the lines 3x-4y+a=0,\ 3x-4y+3a=0,\ 4x-3y-a=0\ a n d \4x-3y-2a =0\ i s (2a^2)/7s qdotu n i t sdot