Distance Between Two Points By Change of Coordinates by Shifting Axes Near Or Far

Let us assume that there are two points in a space (plane surface), 'P' and 'Q'. Let the space be divided into 4 parts by a horizontal line y-axis and by a vertical line x-axis Now what I want propose is:- " Let us consider two cases- case(i): when the plane(space) is divided into 4 parts in such a way that the point 'p' is near to origin and 'Q' is some what far away from origin. Give some readings to the both axes(x,y axes). Now calculate the distance between 'P' and 'Q' (obtained coordinates) using the distance formula, Let the distance be 'R' case(ii):- Now again plot two points in plane with distance 'R'( same above distance). Divide the plane in such a way that the point 'Q' is near to the origin and the point 'P' is some what far away from origin. Now calculate the distance between the obtained coordinates, the distance will be exactly as case(i) distance ie., 'R' , Therefore the coordinates obtained may be different but the distance will be equal ie., case(i)=case(ii) Hence proved Thankyou