A straight line $$L$$ is perpendicular to the line $$5x - y = 1.$$ The area of the triangle formed by the line $$L$$ and the coordinate axes is $$5$$. Find the equation of the Line $$L$$.

(a) Two vertices of a triangle are $$(5, -1)$$ and $$(-2, 3).$$ If the orthocentre of the triangle is the origin, find the coordinates of the third point.
(b) Find the equation of the line which bisects the obtuse angle between the lines $$x - 2y + 4 = 0$$ and $$4x - 3y + 2 = 0$$.

One side of rectangle lies along the line $$4x + 7y + 5 = 0.$$ Two of its vertices are $$(-3, 1)$$ and $$(1, 1).$$ Find the equations of the other three sides.

The area of a triangle is $$5$$. Two of its vertices are $$A\left( {2,1} \right)$$ and $$B\left( {3, - 2} \right)$$. The third vertex $$C$$ lies on $$y = x + 3$$. Find $$C$$.