Area of blue triangle OPQ = area of red rectangle minus the area of the outer three triangles.
= x2y1 – ½ [ (x1 y1 ) + (y2 -y1 )(x1 -x2 ) + (x2 y2 )]
= x2y1 – ½ [ x1 y1 + x1 y2 – x2 y2 – x1y1+ x2 y1 + x2y2]
= x2y1 – ½ [ x1 y2 + x2 y1 ]
= ½ [2 x2y1 – x1 y2 – x2 y1 ]
= ½ [x2y1 – x1 y2 ]
But since either P or Q could be designate (x1y1) or (x2y2) and the triangle can only have a positive area we use the absolute value of what is inside the square brackets to give the area of the blue triangle = ½ | x2y1 – x1 y2 |.