Question

Given a point with coordinates x, y in the xy plane, find its coordinates after each of the following operations: (a) a rotation by /2 about the z axis; (b) a rotation by 26/3 about the z axis; (c) a rotation by 7/2 about the y axis; and (d) a reflection in the yz plane.

Answer 1

Answer: (a) Rotation by π/2 about the z-axis: (-y, x)
(b) Rotation by 2π/3 about the z-axis: (-1/2x - √3/2y, √3/2x - 1/2y)
(c) Rotation by π/2 about the y-axis doesn't change x, y coordinates.
(d) Reflection in the yz plane: (-x, y)