@duerer the point (1, 0, 0) is being mapped to (7, 0, 0), but it is still called (1, 0, 0).
The distance from the Origin to the ‘new’ point (1, 0, 0) is 7.
The distance from the Origin to the ‘new’ point (1/7, 0, 0) is 1:
That is why the sphere intersects the X-axis at (1/7, 0, 0).
When we now rotate around the Y-axis by 90°, the original point (1, 0, 0) is being mapped to (0, 0, 7), but it is still called (1, 0, 0).
So the distance from the Origin to the (scaled and rotated) point (1, 0, 0) is 7.
That is why the sphere still intersects the X-axis at (1/7, 0, 0).
It is difficult to wrap your head around, I know 😉
