Given 4 points of a convex quadrilateral. How to proportionally expand / narrow it relative to the center of gravity?

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2 answers 2

  1. Find the center of gravity.
  2. To draw rays from it to the heights.
  3. On the rays to find points remote from the center of gravity in the desired proportion relative to the old peaks.

    “Proportionally expand / narrow” seems to imply the transformation of a homothety with a center of gravity and a K coefficient.

    Accordingly, you must first calculate the coordinates of the center of gravity (xC, yC) , and then recalculate each vertex (x, y) original polygon as

     x = (x - xC) * K + xC y = (y - yC) * K + yC

    True, it is not clear why we need here 1) the convexity of the quadrilateral and 2) the quadrilaterality of the quadrilateral. The solution does not use any convexity or number of vertices.