A triangle is determined by the lines : y+x-6=0, 3y-x + 2 = 0, 3y = 5x +2. Find the co-ordinates of its orthocentre.

The sides of quadrilateral taken in order, are given by 3x + 11y -65 =0, 5x +y-39 = 0, -x + 5y + 13 = 0 and 11x-3y + 65 = 0 . Find the co-ordinates of the vertices of the quadrilateral.

statement 1: incentre of the triangle formed by the lines whose 3x+4y = 0 , 5x-12y=0 and y - 15 = 0 is the point P whose co-ordinates are (1, 8) . Statement- 2: Point P is equidistant from the 3 lines forming the triangle.

Find the acute angles between the st. lines : y-3x-5=0 and 3y -x +6= 0 .

The sides of a triangle are given by : x-2y+9=0, 3x + y-22 =0 and x + 5y+2=0. Find the vertices of the triangle.

The lines x-y-6=0, 4x-3y-20=0 and 6x+5y+8=0 are:

Find the acute angles between the st. lines : y-sqrt3 x-5=0 and 3y-x+6=0 .

Find the angle between the lines: x-2y+z=0=x+2y-2z and x+2y+z=0=3x+9y+5z .

Orthocentre of the triangle formed by the lines xy-3x-5y+15=0 and 3x+5y=15 is

Find the area of the triangle formed by the straight lines 7x-2y+10=0, 7x+2y-10=0 and 9x+y+2=0 (without sloving the vertices of the triangle).