For points `P = (x_1, y_1) and Q = (x_2,y_2)` of the coordinate plane, a new distance `d (P, Q)` is defined by `d(P,Q)=|x_1-x_2|+|y_1-y_2|.` Let `O (0, 0)` and `A = (3, 2)`. Prove that the set of points in the first quadrant which are equidistant (wrt 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.