How to calculate the rotation coordinates of two objects in order to maintain their position relative to each other?

Question

Mathematics

There are 2 blocks (red and black)
If we rotate both by 90 degrees, the position relative to each other will change.
but it is necessary to save the
ps position and the angle of rotation may differ.

Answer 1

Pivot point in English is the point around which the turn is made. See wiki:Rotate .
In order for the relative position of the two figures to be preserved during rotation, it is necessary that the "pivots" of both figures coincide.
It is not yet clear from the question what is given and what needs to be found. But suppose we are given two shapes, red (K) and black (H), and we need to rotate both around the center of the red one.
With red, everything is clear. On black, you will need to find the position of the center K before turning. And rotate H about this point.

Answer 2

Rotate the black block's coordinate system.
That is, you must take into account the properties of objects in the desired coordinate system - hierarchically: the way they inherit properties (rotations, stretches, etc.).
When one object is its coordinate system.
When a group - the relative coordinate system for all related child objects is calculated and then it is rotated, etc.