How to increase the scale of a quadrilateral not proportionally?

Question

Mathematics

Given four 2D coordinates A,B,C,D describing a quadrangle (sides may not be equal) which is rotated at an unknown angle. It is not difficult to scale proportionally Fig.1., but it is necessary to increase the size of the quadrangle by a certain factor, so that each of the sides of the rectangle increases by an equal amount in Fig.2. Please tell me how this can be done quickly, a small error of up to 5% is possible. Speed ​​is an important factor.
A,B,C,D are given - you need to find A1, B1, C1, D1

Answer 1

1) find the coordinates of points E and F located on the median line of the original rectangle and at the same time on the bisectors of its corners;
2) the desired points A1, D1 and B1, C1 will be the ends of the proportionally increased vectors EA, ED, FB, FC, respectively