For points $$P\,\,\, = \left( {{x_1},\,{y_1}} \right)$$ and $$Q\,\,\, = \left( {{x_2},\,{y_2}} \right)$$ of the co-ordinate plane, a new distance $$d\left( {P,\,Q} \right)$$ is defined by $$d\left( {P,\,Q} \right)$$$$ = \left( {{x_2},\,{y_2}} \right)\left| {{x_1} - {x_2}} \right| + \left| {{y_1} - {y_2}} \right|.$$ Let $$O = (0, 0)$$ and $$A = (3, 2)$$. Prove that the set of points in the first quadrant which are equidistant (with respect to the new distance) from $$O$$ and $$A$$ consists of the union of a line segment of finite length and an infinite ray. Sketch this set in a labelled diagram.