Rotation about the origin is commonly described as a rigid transformation in the plane.
a. (i) What is meant by a rigid transformation? Give one example other than rotation.
b. (ii) Show algebraically that the distance of any point from the origin remains unchanged after rotation through an angle θ about the origin.
c. (iii) Hence state the locus of all possible images of a fixed point when it is rotated through every possible angle about the origin.