Transform 2d object by two points gained from touch

Hi,

Could someone explain or give a code example how to make 2d gameobject transform (canvas ui image) in that way:

1. when you put two fingers on gameobject, remember local positions where fingers touches the gameobject.

2. when you are moving fingers on screen (any finger, both fingers, any direction), they pointing into the same points of gameobject all the time, but game object transforms (rotates, scale, move).

I know, that can be achieved by calculating separately distance, angle and scale, but my question is, is there any mathematical way to gain such translations into one mathematical formula?

Ideal example of this is a Android Google Maps Application, as you can see in this app, when you touch screen with two fingers, whatever you do (rotate, scale, move), that fingers always pointing to the same points. How to achieve such behaviour?

Can someone help me with this?