I would like to find out a formula (mathematical equation(s)) for adjusting the position of any point enclosed in a rectangle when its corner point is repositioned such that (1) all other corner points remain in their place, and (2) all interior and boundary points are repositioned proportionally. This operation is typically associated with readjusting the bounding-box of a 2d polygon in a manner that "stretches" the polygon.
Let's say Ptl is the top-left corner of a bounding-box of a polygon and the point's location is (x,y) in Cartesian coordinates. Let's say the point is moved by (dx,dy), ie this point's new location is now Ptl'=(x+dx,y+dy). However, the three remaining corner points of the rectangle remain in their positions. If P is any point within the original rectangle, what will its new position be?