Question

How to find point of rotation in transformation?

Answer 1

Answer:

This point can be inside the figure, in which case the figure stays where it is and just spins. Or the point can be outside the figure, in which case the figure moves along a circular arc (like an orbit) around the center of rotation. The amount of turning is called the rotation angle.

The easiest way to understand this is by doing a problem: In the following figure, pre-image triangle ABC has been rotated to create image triangle A’B’C’. Find the center of rotation.

geometry-rotation-center

To begin, take the three segments that connect pre-image points to their image points (in this case, line AA’, line BB’, and line CC’). In all rotations, the center of rotation lies at the intersection of the perpendicular bisectors of such segments. Because the three perpendicular bisectors meet at the same point, you need only two of them to find the point of intersection. Any two will work, so find the perpendicular bisectors of lines AA’ and BB’; then you can set their equations equal to each other to find where they intersect.