Answer the following conceptual questions related to a triangle whose vertices are (x1,y1), (x2,y2) and (x3,y3) in the Cartesian plane.
(i) Write an expression for S, defined as twice the area of the triangle when the sign of the expression is retained.
(ii) Explain how the sign of S is related to whether the vertices are listed in clockwise or anticlockwise order.
(iii) Describe a systematic way to rearrange the three vertices so that the value of S becomes positive without altering the shape or size of the triangle.